Question

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

score 270 · Answer 1 · 2026-05-10 16:13:16

270

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

Published on 10 May 2026 - 16:13

score 322 · Answer 2 · 2026-04-13 15:49:44

322

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

Published on 13 Apr 2026 - 15:49

score 44 · Answer 3 · 2026-05-10 15:45:43

44

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Infinite sum of antisymmetric matrix?

Published on 10 May 2026 - 15:45

score 92 · Answer 4 · 2026-04-13 22:11:19

92

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

Published on 13 Apr 2026 - 22:11

score 62 · Answer 5 · 2026-05-10 15:47:56

62

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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 10 May 2026 - 15:47

score 85 · Answer 6 · 2026-05-10 13:50:26

85

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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 10 May 2026 - 13:50

score 173 · Answer 7 · 2026-05-10 23:39:30

173

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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 10 May 2026 - 23:39

score 2k · Answer 8 · 2026-04-18 00:02:13

2k

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

Published on 18 Apr 2026 - 0:02

score 194 · Answer 9 · 2026-05-10 19:35:14

194

Views

A naive conjecture about Taylor series convergence

Published on 10 May 2026 - 19:35

score 540 · Answer 10 · 2026-05-05 23:29:02

540

Views

Laurent Series problems

Published on 05 May 2026 - 23:29

score 93 · Answer 11 · 2026-04-16 13:37:03

93

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

Published on 16 Apr 2026 - 13:37

score 1.4k · Answer 12 · 2026-04-14 10:45:08

1.4k

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

Published on 14 Apr 2026 - 10:45

score 41 · Answer 13 · 2026-04-17 07:01:54

41

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

Published on 17 Apr 2026 - 7:01

score 493 · Answer 14 · 2026-05-10 15:45:58

493

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

Published on 10 May 2026 - 15:45

score 304 · Answer 15 · 2026-05-11 00:39:01

304

Views

Using Taylor Series in Lebesgue Integral.

Published on 11 May 2026 - 0:39

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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