Question

Evaluating $\lim_{x\to0}\frac{x\sin{(\sin{x})}-\sin^2{x}}{x^6}$

score 267 · Answer 1 · 2026-03-24 23:46:02

267

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Evaluating $\lim_{x\to0}\frac{x\sin{(\sin{x})}-\sin^2{x}}{x^6}$

Published on 24 Mar 2026 - 23:46

score 319 · Answer 2 · 2018-02-02 21:33:06

319

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Example of function whose derivatives grow faster than it's Taylor Polynomial Error?

Published on 02 Feb 2018 - 21:33

score 41 · Answer 3 · 2026-03-25 19:03:21

41

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Infinite sum of antisymmetric matrix?

Published on 25 Mar 2026 - 19:03

score 90 · Answer 4 · 2018-02-03 02:54:56

90

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Taylor's Theorem: equality between the function and the infinite series

Published on 03 Feb 2018 - 2:54

score 59 · Answer 5 · 2026-03-24 22:07:40

59

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Is it true that $\left\lvert e^z-\sum\limits_{k=0}^{10T}\frac{z^k}{k!}\right\rvert\le e^{-9T}$ for every $\lvert z\rvert\le T$

Published on 24 Mar 2026 - 22:07

score 84 · Answer 6 · 2026-03-24 22:51:54

84

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Let $f$ a function with bounded partial derivatives. Find the greatest value that $f$ can achieve at point $(1, 2)$

Published on 24 Mar 2026 - 22:51

score 170 · Answer 7 · 2026-03-25 15:52:42

170

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Proving that if $\lim\limits_{x\to\infty} xf(x)=0$ and $\lim\limits_{x\to\infty}xf''(x)=0$ , then $\lim\limits_{x\to\infty}xf'(x)=0$. (using Taylor)

Published on 25 Mar 2026 - 15:52

score 2k · Answer 8 · 2018-02-05 02:08:46

2k

Views

Radius of convergence of $\frac{1}{\cosh(z)}$

Published on 05 Feb 2018 - 2:08

score 191 · Answer 9 · 2026-03-25 06:01:24

191

Views

A naive conjecture about Taylor series convergence

Published on 25 Mar 2026 - 6:01

score 529 · Answer 10 · 2026-03-25 13:05:32

529

Views

Laurent Series problems

Published on 25 Mar 2026 - 13:05

score 90 · Answer 11 · 2018-02-05 23:37:40

90

Views

Limit of $\frac{x^2-\log(1+x^2)}{x^2\sin^2x}$ as $x$ goes to $0$

Published on 05 Feb 2018 - 23:37

score 1.4k · Answer 12 · 2018-02-06 11:29:19

1.4k

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Approximating $\sin 2$ with an error of less than $0.001$

Published on 06 Feb 2018 - 11:29

score 36 · Answer 13 · 2018-02-06 15:53:37

36

Views

A few notations about Taylor Expansion in Empirical Likelihood by Owen.

Published on 06 Feb 2018 - 15:53

score 490 · Answer 14 · 2026-03-25 01:26:14

490

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Can I show the error of the trapezoidal approximation using big-O limits?

Published on 25 Mar 2026 - 1:26

score 301 · Answer 15 · 2026-03-25 01:35:25

301

Views

Using Taylor Series in Lebesgue Integral.

Published on 25 Mar 2026 - 1:35

List Question

Evaluating $\lim_{x\to0}\frac{x\sin{(\sin{x})}-\sin^2{x}}{x^6}$

Example of function whose derivatives grow faster than it's Taylor Polynomial Error?

Infinite sum of antisymmetric matrix?

Taylor's Theorem: equality between the function and the infinite series

Is it true that $\left\lvert e^z-\sum\limits_{k=0}^{10T}\frac{z^k}{k!}\right\rvert\le e^{-9T}$ for every $\lvert z\rvert\le T$

Let $f$ a function with bounded partial derivatives. Find the greatest value that $f$ can achieve at point $(1, 2)$

Proving that if $\lim\limits_{x\to\infty} xf(x)=0$ and $\lim\limits_{x\to\infty}xf''(x)=0$ , then $\lim\limits_{x\to\infty}xf'(x)=0$. (using Taylor)

Radius of convergence of $\frac{1}{\cosh(z)}$

A naive conjecture about Taylor series convergence

Laurent Series problems

Limit of $\frac{x^2-\log(1+x^2)}{x^2\sin^2x}$ as $x$ goes to $0$

Approximating $\sin 2$ with an error of less than $0.001$

A few notations about Taylor Expansion in Empirical Likelihood by Owen.

Can I show the error of the trapezoidal approximation using big-O limits?

Using Taylor Series in Lebesgue Integral.

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