Index
stringlengths 1
5
| Challenge
stringlengths 41
1.55k
| Answer in Latex
stringclasses 122
values | Answer in Sympy
stringlengths 1
774
| Variation
stringclasses 31
values | Source
stringclasses 61
values |
|---|---|---|---|---|---|
401 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(9997025\right) n \cdot ( \left(3399363\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(8635398\right) n \cdot ( \left(3399363\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*3399363**n, (n, 2, oo))*8635398*9997025/6 | Numeric-All-7 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
402 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(50849136\right) n \cdot ( \left(49317708\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(38518091\right) n \cdot ( \left(49317708\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*49317708**n, (n, 2, oo))*38518091*50849136/6 | Numeric-All-8 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
403 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(597140185\right) n \cdot ( \left(908557767\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(130111075\right) n \cdot ( \left(908557767\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*908557767**n, (n, 2, oo))*130111075*597140185/6 | Numeric-All-9 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
404 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(7136646496\right) n \cdot ( \left(3240980819\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(3618373856\right) n \cdot ( \left(3240980819\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*3240980819**n, (n, 2, oo))*3618373856*7136646496/6 | Numeric-All-10 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
405 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left(B n \cdot (F x)^n\right$ | B*Sum(F**n*n*x**n*(n**2 - 1), (n, 2, oo))/6 | Symbolic-2 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
406 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left(A n \cdot (F x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right$ | A*Sum(F**n*n*x**n*(n**2 - 1), (n, 2, oo))/6 | Symbolic-2 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
407 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left(A n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left(B n \cdot ( x)^n\right$ | A*B*Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Symbolic-2 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
408 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right$ | Sum(F**n*n*x**n*(n**2 - 1), (n, 2, oo))/6 | Symbolic-1 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
409 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left(B n \cdot ( x)^n\right$ | B*Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Symbolic-1 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
410 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left(A n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | A*Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Symbolic-1 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
411 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
412 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
413 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
414 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
415 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
416 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
417 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
418 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
419 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
420 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
421 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
422 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
423 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
424 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
425 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
426 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
427 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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428 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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429 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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430 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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431 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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432 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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433 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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434 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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435 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
436 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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437 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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438 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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439 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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440 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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441 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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442 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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443 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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444 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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445 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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446 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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447 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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448 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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449 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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450 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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451 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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452 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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453 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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454 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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455 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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456 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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457 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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458 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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459 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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460 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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461 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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462 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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463 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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464 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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465 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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466 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
467 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
468 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
469 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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470 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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471 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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472 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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473 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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474 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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475 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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476 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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477 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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478 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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479 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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480 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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481 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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482 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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483 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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484 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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485 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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486 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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487 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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488 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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489 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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490 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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491 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
492 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
493 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
494 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
495 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
496 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
497 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
498 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
499 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Easy | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
|
500 | Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$ | sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2 | Equivalence-All-Hard | U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921 |
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