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
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|---|---|---|---|---|---|
501
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
502
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
503
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
504
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
505
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
506
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
507
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
508
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
509
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
510
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
511
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
512
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
513
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
514
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
515
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
516
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
517
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
518
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
519
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
520
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
521
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
522
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
523
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
524
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
525
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
526
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
527
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
528
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
529
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
530
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
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
|
|
531
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
532
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
533
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
534
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
535
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
536
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
537
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
538
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
539
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
540
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
541
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(1\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(1\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5*1**5/2 + 5*sqrt(2)*x**4*1**4/2 - 10*sqrt(2)*x**3*1**3 - 30*sqrt(2)*x**2*1**2 + 60*sqrt(2)*x*1 + 60*sqrt(2))/120
|
Numeric-One-1
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
542
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(70\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(70\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5*70**5/2 + 5*sqrt(2)*x**4*70**4/2 - 10*sqrt(2)*x**3*70**3 - 30*sqrt(2)*x**2*70**2 + 60*sqrt(2)*x*70 + 60*sqrt(2))/120
|
Numeric-One-2
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
543
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(942\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(942\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5*942**5/2 + 5*sqrt(2)*x**4*942**4/2 - 10*sqrt(2)*x**3*942**3 - 30*sqrt(2)*x**2*942**2 + 60*sqrt(2)*x*942 + 60*sqrt(2))/120
|
Numeric-One-3
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
544
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(1641\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(1641\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5*1641**5/2 + 5*sqrt(2)*x**4*1641**4/2 - 10*sqrt(2)*x**3*1641**3 - 30*sqrt(2)*x**2*1641**2 + 60*sqrt(2)*x*1641 + 60*sqrt(2))/120
|
Numeric-One-4
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
545
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(73820\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(73820\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5*73820**5/2 + 5*sqrt(2)*x**4*73820**4/2 - 10*sqrt(2)*x**3*73820**3 - 30*sqrt(2)*x**2*73820**2 + 60*sqrt(2)*x*73820 + 60*sqrt(2))/120
|
Numeric-One-5
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
546
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(729380\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(729380\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5*729380**5/2 + 5*sqrt(2)*x**4*729380**4/2 - 10*sqrt(2)*x**3*729380**3 - 30*sqrt(2)*x**2*729380**2 + 60*sqrt(2)*x*729380 + 60*sqrt(2))/120
|
Numeric-One-6
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
547
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(7539862\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(7539862\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5*7539862**5/2 + 5*sqrt(2)*x**4*7539862**4/2 - 10*sqrt(2)*x**3*7539862**3 - 30*sqrt(2)*x**2*7539862**2 + 60*sqrt(2)*x*7539862 + 60*sqrt(2))/120
|
Numeric-One-7
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
548
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(41291637\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(41291637\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5*41291637**5/2 + 5*sqrt(2)*x**4*41291637**4/2 - 10*sqrt(2)*x**3*41291637**3 - 30*sqrt(2)*x**2*41291637**2 + 60*sqrt(2)*x*41291637 + 60*sqrt(2))/120
|
Numeric-One-8
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
549
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(557323903\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(557323903\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5*557323903**5/2 + 5*sqrt(2)*x**4*557323903**4/2 - 10*sqrt(2)*x**3*557323903**3 - 30*sqrt(2)*x**2*557323903**2 + 60*sqrt(2)*x*557323903 + 60*sqrt(2))/120
|
Numeric-One-9
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
550
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( \left(7692533293\right) x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( \left(7692533293\right) x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5*7692533293**5/2 + 5*sqrt(2)*x**4*7692533293**4/2 - 10*sqrt(2)*x**3*7692533293**3 - 30*sqrt(2)*x**2*7692533293**2 + 60*sqrt(2)*x*7692533293 + 60*sqrt(2))/120
|
Numeric-One-10
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
551
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
552
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
553
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
554
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
555
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
556
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
557
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
558
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
559
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
560
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
561
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(2\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(2\right) \pi }{ 4 }\right)\right)$
|
(x**5*cos(pi*2/4) + 5*x**4*sin(pi*2/4) - 20*x**3*cos(pi*2/4) - 60*x**2*sin(pi*2/4) + 120*x*cos(pi*2/4) + 120*sin(pi*2/4))/120
|
Numeric-One-1
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
562
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(36\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(36\right) \pi }{ 4 }\right)\right)$
|
(x**5*cos(pi*36/4) + 5*x**4*sin(pi*36/4) - 20*x**3*cos(pi*36/4) - 60*x**2*sin(pi*36/4) + 120*x*cos(pi*36/4) + 120*sin(pi*36/4))/120
|
Numeric-One-2
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
563
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(119\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(119\right) \pi }{ 4 }\right)\right)$
|
(x**5*cos(pi*119/4) + 5*x**4*sin(pi*119/4) - 20*x**3*cos(pi*119/4) - 60*x**2*sin(pi*119/4) + 120*x*cos(pi*119/4) + 120*sin(pi*119/4))/120
|
Numeric-One-3
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
564
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(3052\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(3052\right) \pi }{ 4 }\right)\right)$
|
(x**5*cos(pi*3052/4) + 5*x**4*sin(pi*3052/4) - 20*x**3*cos(pi*3052/4) - 60*x**2*sin(pi*3052/4) + 120*x*cos(pi*3052/4) + 120*sin(pi*3052/4))/120
|
Numeric-One-4
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
565
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(13938\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(13938\right) \pi }{ 4 }\right)\right)$
|
(x**5*cos(pi*13938/4) + 5*x**4*sin(pi*13938/4) - 20*x**3*cos(pi*13938/4) - 60*x**2*sin(pi*13938/4) + 120*x*cos(pi*13938/4) + 120*sin(pi*13938/4))/120
|
Numeric-One-5
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
566
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(843759\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(843759\right) \pi }{ 4 }\right)\right)$
|
(x**5*cos(pi*843759/4) + 5*x**4*sin(pi*843759/4) - 20*x**3*cos(pi*843759/4) - 60*x**2*sin(pi*843759/4) + 120*x*cos(pi*843759/4) + 120*sin(pi*843759/4))/120
|
Numeric-One-6
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
567
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(9308594\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(9308594\right) \pi }{ 4 }\right)\right)$
|
(x**5*cos(pi*9308594/4) + 5*x**4*sin(pi*9308594/4) - 20*x**3*cos(pi*9308594/4) - 60*x**2*sin(pi*9308594/4) + 120*x*cos(pi*9308594/4) + 120*sin(pi*9308594/4))/120
|
Numeric-One-7
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
568
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(98380748\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(98380748\right) \pi }{ 4 }\right)\right)$
|
(x**5*cos(pi*98380748/4) + 5*x**4*sin(pi*98380748/4) - 20*x**3*cos(pi*98380748/4) - 60*x**2*sin(pi*98380748/4) + 120*x*cos(pi*98380748/4) + 120*sin(pi*98380748/4))/120
|
Numeric-One-8
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
569
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(131490911\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(131490911\right) \pi }{ 4 }\right)\right)$
|
(x**5*cos(pi*131490911/4) + 5*x**4*sin(pi*131490911/4) - 20*x**3*cos(pi*131490911/4) - 60*x**2*sin(pi*131490911/4) + 120*x*cos(pi*131490911/4) + 120*sin(pi*131490911/4))/120
|
Numeric-One-9
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
570
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin( x) \cdot \cos\left(\frac{ \left(3050900991\right) \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \left(3050900991\right) \pi }{ 4 }\right)\right)$
|
(x**5*cos(pi*3050900991/4) + 5*x**4*sin(pi*3050900991/4) - 20*x**3*cos(pi*3050900991/4) - 60*x**2*sin(pi*3050900991/4) + 120*x*cos(pi*3050900991/4) + 120*sin(pi*3050900991/4))/120
|
Numeric-One-10
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
571
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
572
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
573
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
574
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
575
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
576
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
577
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
578
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
579
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
580
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
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-One-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
581
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(9\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5/2 + 5*sqrt(2)*x**4/2 - 10*sqrt(2)*x**3 - 30*sqrt(2)*x**2 + 60*sqrt(2)*x + 60*sqrt(2))*9/120
|
Numeric-One-1
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
582
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(31\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5/2 + 5*sqrt(2)*x**4/2 - 10*sqrt(2)*x**3 - 30*sqrt(2)*x**2 + 60*sqrt(2)*x + 60*sqrt(2))*31/120
|
Numeric-One-2
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
583
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(478\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5/2 + 5*sqrt(2)*x**4/2 - 10*sqrt(2)*x**3 - 30*sqrt(2)*x**2 + 60*sqrt(2)*x + 60*sqrt(2))*478/120
|
Numeric-One-3
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
584
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(1689\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5/2 + 5*sqrt(2)*x**4/2 - 10*sqrt(2)*x**3 - 30*sqrt(2)*x**2 + 60*sqrt(2)*x + 60*sqrt(2))*1689/120
|
Numeric-One-4
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
585
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(44907\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5/2 + 5*sqrt(2)*x**4/2 - 10*sqrt(2)*x**3 - 30*sqrt(2)*x**2 + 60*sqrt(2)*x + 60*sqrt(2))*44907/120
|
Numeric-One-5
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
586
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(441329\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5/2 + 5*sqrt(2)*x**4/2 - 10*sqrt(2)*x**3 - 30*sqrt(2)*x**2 + 60*sqrt(2)*x + 60*sqrt(2))*441329/120
|
Numeric-One-6
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
587
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(2303680\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5/2 + 5*sqrt(2)*x**4/2 - 10*sqrt(2)*x**3 - 30*sqrt(2)*x**2 + 60*sqrt(2)*x + 60*sqrt(2))*2303680/120
|
Numeric-One-7
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
588
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(58813789\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5/2 + 5*sqrt(2)*x**4/2 - 10*sqrt(2)*x**3 - 30*sqrt(2)*x**2 + 60*sqrt(2)*x + 60*sqrt(2))*58813789/120
|
Numeric-One-8
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
589
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(426813842\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5/2 + 5*sqrt(2)*x**4/2 - 10*sqrt(2)*x**3 - 30*sqrt(2)*x**2 + 60*sqrt(2)*x + 60*sqrt(2))*426813842/120
|
Numeric-One-9
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
590
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(7846268737\right) \left(\sin( x) \cdot \cos\left(\frac{ \pi }{ 4 }\right) + \cos( x) \cdot \sin\left(\frac{ \pi }{ 4 }\right)\right)$
|
(sqrt(2)*x**5/2 + 5*sqrt(2)*x**4/2 - 10*sqrt(2)*x**3 - 30*sqrt(2)*x**2 + 60*sqrt(2)*x + 60*sqrt(2))*7846268737/120
|
Numeric-One-10
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
591
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(9\right) \left(\sin( \left(1\right) x) \cdot \cos\left(\frac{ \left(8\right) \pi }{ 4 }\right) + \cos( \left(1\right) x) \cdot \sin\left(\frac{ \left(8\right) \pi }{ 4 }\right)\right)$
|
9*(x**5*cos(pi*8/4)*1**5 + 5*x**4*sin(pi*8/4)*1**4 - 20*x**3*cos(pi*8/4)*1**3 - 60*x**2*sin(pi*8/4)*1**2 + 120*x*cos(pi*8/4)*1 + 120*sin(pi*8/4))/120
|
Numeric-All-1
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
592
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(18\right) \left(\sin( \left(69\right) x) \cdot \cos\left(\frac{ \left(71\right) \pi }{ 4 }\right) + \cos( \left(69\right) x) \cdot \sin\left(\frac{ \left(71\right) \pi }{ 4 }\right)\right)$
|
18*(x**5*cos(pi*71/4)*69**5 + 5*x**4*sin(pi*71/4)*69**4 - 20*x**3*cos(pi*71/4)*69**3 - 60*x**2*sin(pi*71/4)*69**2 + 120*x*cos(pi*71/4)*69 + 120*sin(pi*71/4))/120
|
Numeric-All-2
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
593
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(920\right) \left(\sin( \left(862\right) x) \cdot \cos\left(\frac{ \left(505\right) \pi }{ 4 }\right) + \cos( \left(862\right) x) \cdot \sin\left(\frac{ \left(505\right) \pi }{ 4 }\right)\right)$
|
920*(x**5*cos(pi*505/4)*862**5 + 5*x**4*sin(pi*505/4)*862**4 - 20*x**3*cos(pi*505/4)*862**3 - 60*x**2*sin(pi*505/4)*862**2 + 120*x*cos(pi*505/4)*862 + 120*sin(pi*505/4))/120
|
Numeric-All-3
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
594
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(6305\right) \left(\sin( \left(7619\right) x) \cdot \cos\left(\frac{ \left(7639\right) \pi }{ 4 }\right) + \cos( \left(7619\right) x) \cdot \sin\left(\frac{ \left(7639\right) \pi }{ 4 }\right)\right)$
|
6305*(x**5*cos(pi*7639/4)*7619**5 + 5*x**4*sin(pi*7639/4)*7619**4 - 20*x**3*cos(pi*7639/4)*7619**3 - 60*x**2*sin(pi*7639/4)*7619**2 + 120*x*cos(pi*7639/4)*7619 + 120*sin(pi*7639/4))/120
|
Numeric-All-4
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
595
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(44853\right) \left(\sin( \left(34365\right) x) \cdot \cos\left(\frac{ \left(79699\right) \pi }{ 4 }\right) + \cos( \left(34365\right) x) \cdot \sin\left(\frac{ \left(79699\right) \pi }{ 4 }\right)\right)$
|
44853*(x**5*cos(pi*79699/4)*34365**5 + 5*x**4*sin(pi*79699/4)*34365**4 - 20*x**3*cos(pi*79699/4)*34365**3 - 60*x**2*sin(pi*79699/4)*34365**2 + 120*x*cos(pi*79699/4)*34365 + 120*sin(pi*79699/4))/120
|
Numeric-All-5
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
596
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(800194\right) \left(\sin( \left(954683\right) x) \cdot \cos\left(\frac{ \left(952072\right) \pi }{ 4 }\right) + \cos( \left(954683\right) x) \cdot \sin\left(\frac{ \left(952072\right) \pi }{ 4 }\right)\right)$
|
800194*(x**5*cos(pi*952072/4)*954683**5 + 5*x**4*sin(pi*952072/4)*954683**4 - 20*x**3*cos(pi*952072/4)*954683**3 - 60*x**2*sin(pi*952072/4)*954683**2 + 120*x*cos(pi*952072/4)*954683 + 120*sin(pi*952072/4))/120
|
Numeric-All-6
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
597
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(7149638\right) \left(\sin( \left(6114242\right) x) \cdot \cos\left(\frac{ \left(8274900\right) \pi }{ 4 }\right) + \cos( \left(6114242\right) x) \cdot \sin\left(\frac{ \left(8274900\right) \pi }{ 4 }\right)\right)$
|
7149638*(x**5*cos(pi*8274900/4)*6114242**5 + 5*x**4*sin(pi*8274900/4)*6114242**4 - 20*x**3*cos(pi*8274900/4)*6114242**3 - 60*x**2*sin(pi*8274900/4)*6114242**2 + 120*x*cos(pi*8274900/4)*6114242 + 120*sin(pi*8274900/4))/120
|
Numeric-All-7
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
598
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(67259418\right) \left(\sin( \left(34186104\right) x) \cdot \cos\left(\frac{ \left(55032868\right) \pi }{ 4 }\right) + \cos( \left(34186104\right) x) \cdot \sin\left(\frac{ \left(55032868\right) \pi }{ 4 }\right)\right)$
|
67259418*(x**5*cos(pi*55032868/4)*34186104**5 + 5*x**4*sin(pi*55032868/4)*34186104**4 - 20*x**3*cos(pi*55032868/4)*34186104**3 - 60*x**2*sin(pi*55032868/4)*34186104**2 + 120*x*cos(pi*55032868/4)*34186104 + 120*sin(pi*55032868/4))/120
|
Numeric-All-8
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
599
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(252322481\right) \left(\sin( \left(576517738\right) x) \cdot \cos\left(\frac{ \left(125354911\right) \pi }{ 4 }\right) + \cos( \left(576517738\right) x) \cdot \sin\left(\frac{ \left(125354911\right) \pi }{ 4 }\right)\right)$
|
252322481*(x**5*cos(pi*125354911/4)*576517738**5 + 5*x**4*sin(pi*125354911/4)*576517738**4 - 20*x**3*cos(pi*125354911/4)*576517738**3 - 60*x**2*sin(pi*125354911/4)*576517738**2 + 120*x*cos(pi*125354911/4)*576517738 + 120*sin(pi*125354911/4))/120
|
Numeric-All-9
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
600
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(7225371638\right) \left(\sin( \left(1001065337\right) x) \cdot \cos\left(\frac{ \left(8002114844\right) \pi }{ 4 }\right) + \cos( \left(1001065337\right) x) \cdot \sin\left(\frac{ \left(8002114844\right) \pi }{ 4 }\right)\right)$
|
7225371638*(x**5*cos(pi*8002114844/4)*1001065337**5 + 5*x**4*sin(pi*8002114844/4)*1001065337**4 - 20*x**3*cos(pi*8002114844/4)*1001065337**3 - 60*x**2*sin(pi*8002114844/4)*1001065337**2 + 120*x*cos(pi*8002114844/4)*1001065337 + 120*sin(pi*8002114844/4))/120
|
Numeric-All-10
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
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