Question

How to show that $\cos(x)=\sum\limits_{n=0}^\infty (-1)^n \frac {x^{2n}}{ (2n)!} $

score 71 · Answer 1 · 2014-06-07 12:19:19

71

Views

How to show that $\cos(x)=\sum\limits_{n=0}^\infty (-1)^n \frac {x^{2n}}{ (2n)!} $

Published on 07 Jun 2014 - 12:19

score 51 · Answer 2 · 2014-06-08 05:19:48

51

Views

Maclaurin series stuck at finding $L_n$

Published on 08 Jun 2014 - 5:19

score 281 · Answer 3 · 2014-06-08 16:35:40

281

Views

Two ways to show that $\sin x -x +\frac {x^3}{3!}-\frac {x^5}{5!}< 0$

Published on 08 Jun 2014 - 16:35

score 64 · Answer 4 · 2014-06-09 07:19:43

64

Views

Cubic MacLaurin $e^{x^2}$

Published on 09 Jun 2014 - 7:19

score 77 · Answer 5 · 2014-06-09 08:53:42

77

Views

How can I expand $\frac{1}{\sqrt{1-x^2}}$ by using the binomial series?

Published on 09 Jun 2014 - 8:53

score 130 · Answer 6 · 2014-06-09 09:34:12

130

Views

Expanding $\frac{1}{\sqrt{1-x^2}}$ through the expansion of $\frac{1}{\sqrt{1-x}}$ by binomial series

Published on 09 Jun 2014 - 9:34

score 94 · Answer 7 · 2014-06-09 11:12:12

$f(x)=\begin{cases}e^{\frac{-1}{x^2}} & \text{ if } x\neq 0 \\ 0& \text{ if } x= 0\end{cases}$ is not equal to its Maclaurin Series

score 92 · Answer 8 · 2014-06-09 13:12:17

92

Views

How can I find the Maclaurin series of $\frac{1}{1+x+x^2}$?

Published on 09 Jun 2014 - 13:12

score 2k · Answer 9 · 2026-04-03 00:22:13

2k

Views

Taylor series of $\sin(x)$ converges uniformly on $[-\pi,\pi]$?

Published on 03 Apr 2026 - 0:22

score 91 · Answer 10 · 2014-06-10 05:35:49

91

Views

If $\displaystyle \sum_{n=0}^{\infty}c_{n}x^{n}=0$, show that $c_n= 0$ for any $n$

Published on 10 Jun 2014 - 5:35

score 6.6k · Answer 11 · 2014-06-10 15:02:08

6.6k

Views

When does the remainder term in the taylor series go to zero?

Published on 10 Jun 2014 - 15:02

score 21 · Answer 12 · 2014-06-10 18:16:58

21

Views

taylor series please i need immediate help

Published on 10 Jun 2014 - 18:16

score 32 · Answer 13 · 2014-06-13 17:30:49

32

Views

solution check for approximating derivative using a Taylor expansion.

Published on 13 Jun 2014 - 17:30

score 219 · Answer 14 · 2014-06-14 16:01:24

219

Views

Proving $\forall x\in\mathbb R : \dfrac{e^x + e^{-x}}2 \le e^{\frac{x^2}{2}}$ with Cauchy's MVT

Published on 14 Jun 2014 - 16:01

score 319 · Answer 15 · 2026-03-30 12:25:47

319

Views

Finding $\zeta(4)$ by Taylor series

Published on 30 Mar 2026 - 12:25

List Question

How to show that $\cos(x)=\sum\limits_{n=0}^\infty (-1)^n \frac {x^{2n}}{ (2n)!} $

Maclaurin series stuck at finding $L_n$

Two ways to show that $\sin x -x +\frac {x^3}{3!}-\frac {x^5}{5!}< 0$

Cubic MacLaurin $e^{x^2}$

How can I expand $\frac{1}{\sqrt{1-x^2}}$ by using the binomial series?

Expanding $\frac{1}{\sqrt{1-x^2}}$ through the expansion of $\frac{1}{\sqrt{1-x}}$ by binomial series

$f(x)=\begin{cases}e^{\frac{-1}{x^2}} & \text{ if } x\neq 0 \\ 0& \text{ if } x= 0\end{cases}$ is not equal to its Maclaurin Series

How can I find the Maclaurin series of $\frac{1}{1+x+x^2}$?

Taylor series of $\sin(x)$ converges uniformly on $[-\pi,\pi]$?

If $\displaystyle \sum_{n=0}^{\infty}c_{n}x^{n}=0$, show that $c_n= 0$ for any $n$

When does the remainder term in the taylor series go to zero?

taylor series please i need immediate help

solution check for approximating derivative using a Taylor expansion.

Proving $\forall x\in\mathbb R : \dfrac{e^x + e^{-x}}2 \le e^{\frac{x^2}{2}}$ with Cauchy's MVT

Finding $\zeta(4)$ by Taylor series

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