Question

Taylor expansion of the Error function

score 1.3k · Answer 1 · 2014-12-18 17:44:22

1.3k

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Taylor expansion of the Error function

Published on 18 Dec 2014 - 17:44

score 198 · Answer 2 · 2014-12-19 00:18:38

198

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McLaurin series expansion to evaluate a function

Published on 19 Dec 2014 - 0:18

score 114 · Answer 3 · 2026-04-04 13:43:59

114

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$G_n:=\sqrt{n} \left(X_n-1\right) \xrightarrow[n]{d} N(\mu,\sigma^2) $ implies $\sqrt{n} \left(1-X_n^{-1}\right)=G_n+o_P(1)$

Published on 04 Apr 2026 - 13:43

score 2.1k · Answer 4 · 2026-03-25 06:02:04

2.1k

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How is Taylor expansion a generalization of linear approximation?

Published on 25 Mar 2026 - 6:02

score 351 · Answer 5 · 2026-03-28 22:28:32

351

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Using the Maclaurin series to approximate $f(0.1)$ for $f(x)=(3+e^{2x})^{0.5}$

Published on 28 Mar 2026 - 22:28

score 198 · Answer 6 · 2014-12-23 17:31:27

198

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proof for zero function

Published on 23 Dec 2014 - 17:31

score 572 · Answer 7 · 2014-12-24 15:55:31

572

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Equivalence of $\pi$ is the first positive zero of the taylor series for $\sin(x)$ and $\pi/4 = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots$

Published on 24 Dec 2014 - 15:55

score 221 · Answer 8 · 2026-03-29 08:15:55

221

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Find the radius of convergence of the Taylor series of $f(x) = \frac{x-3}{x+2}\ln(5+x)$ at $x=0$

Published on 29 Mar 2026 - 8:15

score 49 · Answer 9 · 2014-12-27 16:20:08

49

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Finding Maclaurin series grade 4

Published on 27 Dec 2014 - 16:20

score 2.7k · Answer 10 · 2014-12-27 17:02:23

2.7k

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Maclaurin series of $\arctan(x)$ up to degree $4$

Published on 27 Dec 2014 - 17:02

score 60 · Answer 11 · 2014-12-27 19:32:27

60

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Expand and hence find (Series)

Published on 27 Dec 2014 - 19:32

score 94 · Answer 12 · 2014-12-27 23:40:56

94

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Can a Taylor Series converge at a point when the remainder term cannot be bounded?

Published on 27 Dec 2014 - 23:40

score 72 · Answer 13 · 2014-12-28 20:02:36

72

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$\frac{f(x)-f(0)}{g(x)-g(0)}=\frac{f'(\nu(x))}{g'(\nu(x))} $ ,the value of the limit: $\lim_{x \to 0^+} \frac{\nu(x)}{x} $

Published on 28 Dec 2014 - 20:02

score 446 · Answer 14 · 2014-12-31 00:56:53

446

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Convergence of the Power Series of $\log(1+\sin x)$

Published on 31 Dec 2014 - 0:56

score 729 · Answer 15 · 2014-12-31 17:37:56

729

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If all derivatives of $f$ are uniformly bounded by a common constant and $f(1/n) = 0$ for all $n$, is $f$ identically zero?

Published on 31 Dec 2014 - 17:37

List Question

Taylor expansion of the Error function

McLaurin series expansion to evaluate a function

$G_n:=\sqrt{n} \left(X_n-1\right) \xrightarrow[n]{d} N(\mu,\sigma^2) $ implies $\sqrt{n} \left(1-X_n^{-1}\right)=G_n+o_P(1)$

How is Taylor expansion a generalization of linear approximation?

Using the Maclaurin series to approximate $f(0.1)$ for $f(x)=(3+e^{2x})^{0.5}$

proof for zero function

Equivalence of $\pi$ is the first positive zero of the taylor series for $\sin(x)$ and $\pi/4 = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots$

Find the radius of convergence of the Taylor series of $f(x) = \frac{x-3}{x+2}\ln(5+x)$ at $x=0$

Finding Maclaurin series grade 4

Maclaurin series of $\arctan(x)$ up to degree $4$

Expand and hence find (Series)

Can a Taylor Series converge at a point when the remainder term cannot be bounded?

$\frac{f(x)-f(0)}{g(x)-g(0)}=\frac{f'(\nu(x))}{g'(\nu(x))} $ ,the value of the limit: $\lim_{x \to 0^+} \frac{\nu(x)}{x} $

Convergence of the Power Series of $\log(1+\sin x)$

If all derivatives of $f$ are uniformly bounded by a common constant and $f(1/n) = 0$ for all $n$, is $f$ identically zero?

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