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 |
|---|---|---|---|---|---|
1001
|
Evaluate
$ \lim_{x \to 0^+} \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \left( \frac{ \tan\left( \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x}{2} \right) }{ \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x}{2} } \right)^{ \frac{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) 3}{( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1002
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x}{2} \right) }{ \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x}{2} } \right)^{ \frac{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) 3}{( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1003
|
Evaluate
$ \lim_{x \to 0^+} \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \left( \frac{ \tan\left( \frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x}{2} \right) }{ \frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x}{2} } \right)^{ \frac{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) 3}{( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1004
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x}{2} \right) }{ \frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x}{2} } \right)^{ \frac{ \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) 3}{( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1005
|
Evaluate
$ \lim_{x \to 0^+} \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \left( \frac{ \tan\left( \frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x}{2} \right) }{ \frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x}{2} } \right)^{ \frac{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) 3}{( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1006
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x}{2} \right) }{ \frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x}{2} } \right)^{ \frac{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) 3}{( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1007
|
Evaluate
$ \lim_{x \to 0^+} \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \left( \frac{ \tan\left( \frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x}{2} \right) }{ \frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x}{2} } \right)^{ \frac{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) 3}{( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1008
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x}{2} \right) }{ \frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x}{2} } \right)^{ \frac{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) 3}{( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1009
|
Evaluate
$ \lim_{x \to 0^+} \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \left( \frac{ \tan\left( \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x}{2} \right) }{ \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x}{2} } \right)^{ \frac{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) 3}{( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1010
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x}{2} \right) }{ \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x}{2} } \right)^{ \frac{ \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) 3}{( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1011
|
Evaluate
$ \lim_{x \to 0^+} \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \left( \frac{ \tan\left( \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x}{2} \right) }{ \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x}{2} } \right)^{ \frac{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) 3}{( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1012
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x}{2} \right) }{ \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x}{2} } \right)^{ \frac{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) 3}{( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1013
|
Evaluate
$ \lim_{x \to 0^+} \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \left( \frac{ \tan\left( \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x}{2} \right) }{ \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x}{2} } \right)^{ \frac{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) 3}{( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1014
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x}{2} \right) }{ \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x}{2} } \right)^{ \frac{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) 3}{( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1015
|
Evaluate
$ \lim_{x \to 0^+} \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1016
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1017
|
Evaluate
$ \lim_{x \to 0^+} \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1018
|
Evaluate
$ \lim_{x \to 0^+} \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1019
|
Evaluate
$ \lim_{x \to 0^+} \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1020
|
Evaluate
$ \lim_{x \to 0^+} \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1021
|
Evaluate
$ \lim_{x \to 0^+} \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1022
|
Evaluate
$ \lim_{x \to 0^+} \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1023
|
Evaluate
$ \lim_{x \to 0^+} \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1024
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1025
|
Evaluate
$ \lim_{x \to 0^+} \left(8\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)*8
|
Numeric-One-1
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1026
|
Evaluate
$ \lim_{x \to 0^+} \left(23\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)*23
|
Numeric-One-2
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1027
|
Evaluate
$ \lim_{x \to 0^+} \left(948\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)*948
|
Numeric-One-3
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1028
|
Evaluate
$ \lim_{x \to 0^+} \left(9522\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)*9522
|
Numeric-One-4
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1029
|
Evaluate
$ \lim_{x \to 0^+} \left(61581\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)*61581
|
Numeric-One-5
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1030
|
Evaluate
$ \lim_{x \to 0^+} \left(496523\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)*496523
|
Numeric-One-6
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1031
|
Evaluate
$ \lim_{x \to 0^+} \left(9246368\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)*9246368
|
Numeric-One-7
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1032
|
Evaluate
$ \lim_{x \to 0^+} \left(39961200\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)*39961200
|
Numeric-One-8
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1033
|
Evaluate
$ \lim_{x \to 0^+} \left(182908068\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)*182908068
|
Numeric-One-9
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1034
|
Evaluate
$ \lim_{x \to 0^+} \left(6957566223\right) \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
e**(1/4)*6957566223
|
Numeric-One-10
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1035
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x}{2} \right) }{ \frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x}{2} } \right)^{ \frac{ 3}{( \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1036
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\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) x}{2} \right) }{ \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) x}{2} } \right)^{ \frac{ 3}{( \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) x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1037
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x}{2} \right) }{ \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x}{2} } \right)^{ \frac{ 3}{( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1038
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x}{2} \right) }{ \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x}{2} } \right)^{ \frac{ 3}{( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1039
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x}{2} \right) }{ \frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x}{2} } \right)^{ \frac{ 3}{( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1040
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x}{2} \right) }{ \frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x}{2} } \right)^{ \frac{ 3}{( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1041
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x}{2} \right) }{ \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x}{2} } \right)^{ \frac{ 3}{( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1042
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x}{2} \right) }{ \frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x}{2} } \right)^{ \frac{ 3}{( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1043
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x}{2} \right) }{ \frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x}{2} } \right)^{ \frac{ 3}{( \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1044
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\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) x}{2} \right) }{ \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) x}{2} } \right)^{ \frac{ 3}{( \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) x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1045
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(6\right) x}{2} \right) }{ \frac{ \left(6\right) x}{2} } \right)^{ \frac{ 3}{( \left(6\right) x)^2} } $
|
e**(1/4)
|
Numeric-One-1
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1046
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(73\right) x}{2} \right) }{ \frac{ \left(73\right) x}{2} } \right)^{ \frac{ 3}{( \left(73\right) x)^2} } $
|
e**(1/4)
|
Numeric-One-2
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1047
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(735\right) x}{2} \right) }{ \frac{ \left(735\right) x}{2} } \right)^{ \frac{ 3}{( \left(735\right) x)^2} } $
|
e**(1/4)
|
Numeric-One-3
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1048
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(4262\right) x}{2} \right) }{ \frac{ \left(4262\right) x}{2} } \right)^{ \frac{ 3}{( \left(4262\right) x)^2} } $
|
e**(1/4)
|
Numeric-One-4
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1049
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(69656\right) x}{2} \right) }{ \frac{ \left(69656\right) x}{2} } \right)^{ \frac{ 3}{( \left(69656\right) x)^2} } $
|
e**(1/4)
|
Numeric-One-5
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1050
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(708913\right) x}{2} \right) }{ \frac{ \left(708913\right) x}{2} } \right)^{ \frac{ 3}{( \left(708913\right) x)^2} } $
|
e**(1/4)
|
Numeric-One-6
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1051
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(5536552\right) x}{2} \right) }{ \frac{ \left(5536552\right) x}{2} } \right)^{ \frac{ 3}{( \left(5536552\right) x)^2} } $
|
e**(1/4)
|
Numeric-One-7
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1052
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(73464178\right) x}{2} \right) }{ \frac{ \left(73464178\right) x}{2} } \right)^{ \frac{ 3}{( \left(73464178\right) x)^2} } $
|
e**(1/4)
|
Numeric-One-8
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1053
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(262373805\right) x}{2} \right) }{ \frac{ \left(262373805\right) x}{2} } \right)^{ \frac{ 3}{( \left(262373805\right) x)^2} } $
|
e**(1/4)
|
Numeric-One-9
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1054
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ \left(1179608531\right) x}{2} \right) }{ \frac{ \left(1179608531\right) x}{2} } \right)^{ \frac{ 3}{( \left(1179608531\right) x)^2} } $
|
e**(1/4)
|
Numeric-One-10
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1055
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1056
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \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) 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1057
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1058
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1059
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1060
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1061
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1062
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1063
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1064
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \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) 3}{( x)^2} } $
|
e**(1/4)
|
Equivalence-One-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1065
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(9\right) 3}{( x)^2} } $
|
e**(9/4)
|
Numeric-One-1
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1066
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(33\right) 3}{( x)^2} } $
|
e**(33/4)
|
Numeric-One-2
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1067
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(136\right) 3}{( x)^2} } $
|
e**(136/4)
|
Numeric-One-3
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1068
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(5095\right) 3}{( x)^2} } $
|
e**(5095/4)
|
Numeric-One-4
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1069
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(48087\right) 3}{( x)^2} } $
|
e**(48087/4)
|
Numeric-One-5
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1070
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(893023\right) 3}{( x)^2} } $
|
e**(893023/4)
|
Numeric-One-6
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1071
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(9663153\right) 3}{( x)^2} } $
|
e**(9663153/4)
|
Numeric-One-7
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1072
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(88506953\right) 3}{( x)^2} } $
|
e**(88506953/4)
|
Numeric-One-8
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1073
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(845653094\right) 3}{( x)^2} } $
|
e**(845653094/4)
|
Numeric-One-9
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1074
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ \left(7938919552\right) 3}{( x)^2} } $
|
e**(7938919552/4)
|
Numeric-One-10
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1075
|
Evaluate
$ \lim_{x \to 0^+} \left(8\right) \left( \frac{ \tan\left( \frac{ \left(8\right) x}{2} \right) }{ \frac{ \left(8\right) x}{2} } \right)^{ \frac{ \left(1\right) 3}{( \left(8\right) x)^2} } $
|
e**(1/4)*8
|
Numeric-All-1
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1076
|
Evaluate
$ \lim_{x \to 0^+} \left(13\right) \left( \frac{ \tan\left( \frac{ \left(33\right) x}{2} \right) }{ \frac{ \left(33\right) x}{2} } \right)^{ \frac{ \left(84\right) 3}{( \left(33\right) x)^2} } $
|
e**(84/4)*13
|
Numeric-All-2
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1077
|
Evaluate
$ \lim_{x \to 0^+} \left(788\right) \left( \frac{ \tan\left( \frac{ \left(160\right) x}{2} \right) }{ \frac{ \left(160\right) x}{2} } \right)^{ \frac{ \left(521\right) 3}{( \left(160\right) x)^2} } $
|
e**(521/4)*788
|
Numeric-All-3
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1078
|
Evaluate
$ \lim_{x \to 0^+} \left(8593\right) \left( \frac{ \tan\left( \frac{ \left(6904\right) x}{2} \right) }{ \frac{ \left(6904\right) x}{2} } \right)^{ \frac{ \left(2936\right) 3}{( \left(6904\right) x)^2} } $
|
e**(2936/4)*8593
|
Numeric-All-4
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1079
|
Evaluate
$ \lim_{x \to 0^+} \left(96535\right) \left( \frac{ \tan\left( \frac{ \left(17346\right) x}{2} \right) }{ \frac{ \left(17346\right) x}{2} } \right)^{ \frac{ \left(88984\right) 3}{( \left(17346\right) x)^2} } $
|
e**(88984/4)*96535
|
Numeric-All-5
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1080
|
Evaluate
$ \lim_{x \to 0^+} \left(170001\right) \left( \frac{ \tan\left( \frac{ \left(393650\right) x}{2} \right) }{ \frac{ \left(393650\right) x}{2} } \right)^{ \frac{ \left(106445\right) 3}{( \left(393650\right) x)^2} } $
|
e**(106445/4)*170001
|
Numeric-All-6
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1081
|
Evaluate
$ \lim_{x \to 0^+} \left(1978138\right) \left( \frac{ \tan\left( \frac{ \left(3242092\right) x}{2} \right) }{ \frac{ \left(3242092\right) x}{2} } \right)^{ \frac{ \left(4121177\right) 3}{( \left(3242092\right) x)^2} } $
|
e**(4121177/4)*1978138
|
Numeric-All-7
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1082
|
Evaluate
$ \lim_{x \to 0^+} \left(36361256\right) \left( \frac{ \tan\left( \frac{ \left(44827190\right) x}{2} \right) }{ \frac{ \left(44827190\right) x}{2} } \right)^{ \frac{ \left(82367371\right) 3}{( \left(44827190\right) x)^2} } $
|
e**(82367371/4)*36361256
|
Numeric-All-8
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1083
|
Evaluate
$ \lim_{x \to 0^+} \left(549838921\right) \left( \frac{ \tan\left( \frac{ \left(845341381\right) x}{2} \right) }{ \frac{ \left(845341381\right) x}{2} } \right)^{ \frac{ \left(851015272\right) 3}{( \left(845341381\right) x)^2} } $
|
e**(851015272/4)*549838921
|
Numeric-All-9
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1084
|
Evaluate
$ \lim_{x \to 0^+} \left(4602159770\right) \left( \frac{ \tan\left( \frac{ \left(8677284920\right) x}{2} \right) }{ \frac{ \left(8677284920\right) x}{2} } \right)^{ \frac{ \left(2984809551\right) 3}{( \left(8677284920\right) x)^2} } $
|
e**(2984809551/4)*4602159770
|
Numeric-All-10
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1085
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{B x}{2} \right) }{ \frac{B x}{2} } \right)^{ \frac{F 3}{(B x)^2} } $
|
e**(F/4)
|
Symbolic-2
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1086
|
Evaluate
$ \lim_{x \to 0^+} A \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{F 3}{( x)^2} } $
|
A*e**(F/4)
|
Symbolic-2
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1087
|
Evaluate
$ \lim_{x \to 0^+} A \left( \frac{ \tan\left( \frac{B x}{2} \right) }{ \frac{B x}{2} } \right)^{ \frac{ 3}{(B x)^2} } $
|
A*e**(1/4)
|
Symbolic-2
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1088
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{F 3}{( x)^2} } $
|
e**(F/4)
|
Symbolic-1
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1089
|
Evaluate
$ \lim_{x \to 0^+} \left( \frac{ \tan\left( \frac{B x}{2} \right) }{ \frac{B x}{2} } \right)^{ \frac{ 3}{(B x)^2} } $
|
e**(1/4)
|
Symbolic-1
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1090
|
Evaluate
$ \lim_{x \to 0^+} A \left( \frac{ \tan\left( \frac{ x}{2} \right) }{ \frac{ x}{2} } \right)^{ \frac{ 3}{( x)^2} } $
|
A*e**(1/4)
|
Symbolic-1
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
1091
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1092
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ x - 5 \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) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ x }{ 5 \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) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1093
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1094
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ x - 5 \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) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ x }{ 5 \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) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1095
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1096
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ x - 5 \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) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ x }{ 5 \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) }\right) } \right)^{ \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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1097
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1098
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x }{ x - 5 \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) }-\frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) }{ \ln\left(\frac{ x }{ 5 \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) }\right) } \right)^{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1099
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1100
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x }{ x - 5 \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) }-\frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) }{ \ln\left(\frac{ x }{ 5 \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) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
Subsets and Splits
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