Question

Approximation of $ \frac{1 - a x^2} {1 - b x^2} $ for small $x$

score 71 · Answer 1 · 2026-04-16 08:30:54

71

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Approximation of $ \frac{1 - a x^2} {1 - b x^2} $ for small $x$

Published on 16 Apr 2026 - 8:30

score 253 · Answer 2 · 2026-04-14 22:11:16

253

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Does $\frac{1}{1-e^{-\frac{1}{e^x}}} - e^x - \frac{1}{2} $ really explode with oscillatory behavior past $x = 15$?

Published on 14 Apr 2026 - 22:11

score 90 · Answer 3 · 2026-03-26 17:53:42

90

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Power series expansion of $\frac{kx}{(x+1)^k-1}$ at $x=0$

Published on 26 Mar 2026 - 17:53

score 51 · Answer 4 · 2026-04-15 00:38:36

51

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Smoothness of quotient of multivariable smooth function by degree 1 polynomial

Published on 15 Apr 2026 - 0:38

score 118 · Answer 5 · 2026-04-24 01:34:27

118

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Prove the inequality $\frac{|x|^n}{n!} \le e^x +e^{-x}$

Published on 24 Apr 2026 - 1:34

score 55 · Answer 6 · 2026-04-16 01:28:16

55

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Finding MacLaurin polynomial of $\cos{(\log{(1+2x^2)})}$ of 8-th order

Published on 16 Apr 2026 - 1:28

score 596 · Answer 7 · 2026-04-15 15:37:39

596

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Approximate Maclaurin series for $\sqrt x$

Published on 15 Apr 2026 - 15:37

score 87 · Answer 8 · 2026-04-13 17:44:52

87

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Maclaurin series without Bernoulli or Euler numbers?

Published on 13 Apr 2026 - 17:44

score 88 · Answer 9 · 2026-04-16 09:58:35

88

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Prove $\mathrm{e}^{(\Delta -1)t} = \sum_{n \geq 0} \mathrm{e}^{-t}\,(1-\mathrm{e}^{-t})^n\,\frac{\Gamma(\Delta+n)}{\Gamma(\Delta)\,\Gamma(n+1)}$

Published on 16 Apr 2026 - 9:58

score 72 · Answer 10 · 2026-04-12 03:05:02

72

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First three terms of Taylor series expansion of $\exp\{-\frac{1}{(x-a)^2}\}$

Published on 12 Apr 2026 - 3:05

score 73 · Answer 11 · 2026-04-13 06:25:49

73

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Using Taylor Series to approximate pi without using arctan?

Published on 13 Apr 2026 - 6:25

score 45 · Answer 12 · 2026-04-13 23:08:16

45

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Taylor series summation

Published on 13 Apr 2026 - 23:08

score 80 · Answer 13 · 2026-04-13 03:45:41

80

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How do I solve this infinite limit with the help of Taylor/Maclaurin series expansion?

Published on 13 Apr 2026 - 3:45

score 21 · Answer 14 · 2026-04-08 20:52:02

21

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Convergence in probability to 0 and negative exponent

Published on 08 Apr 2026 - 20:52

score 85 · Answer 15 · 2026-04-17 04:02:19

85

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General pattern for the series $S = x + \frac{1}{4}x^3 + \frac{9}{64} x^5 + \frac{25}{256} x^7+ \dots$

Published on 17 Apr 2026 - 4:02

List Question

Approximation of $ \frac{1 - a x^2} {1 - b x^2} $ for small $x$

Does $\frac{1}{1-e^{-\frac{1}{e^x}}} - e^x - \frac{1}{2} $ really explode with oscillatory behavior past $x = 15$?

Power series expansion of $\frac{kx}{(x+1)^k-1}$ at $x=0$

Smoothness of quotient of multivariable smooth function by degree 1 polynomial

Prove the inequality $\frac{|x|^n}{n!} \le e^x +e^{-x}$

Finding MacLaurin polynomial of $\cos{(\log{(1+2x^2)})}$ of 8-th order

Approximate Maclaurin series for $\sqrt x$

Maclaurin series without Bernoulli or Euler numbers?

Prove $\mathrm{e}^{(\Delta -1)t} = \sum_{n \geq 0} \mathrm{e}^{-t}\,(1-\mathrm{e}^{-t})^n\,\frac{\Gamma(\Delta+n)}{\Gamma(\Delta)\,\Gamma(n+1)}$

First three terms of Taylor series expansion of $\exp\{-\frac{1}{(x-a)^2}\}$

Using Taylor Series to approximate pi without using arctan?

Taylor series summation

How do I solve this infinite limit with the help of Taylor/Maclaurin series expansion?

Convergence in probability to 0 and negative exponent

General pattern for the series $S = x + \frac{1}{4}x^3 + \frac{9}{64} x^5 + \frac{25}{256} x^7+ \dots$

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