Question

What is the coefficient of $x^7$ in the Taylor series expansion, around $x=0$ of the function $f(x)=\sin^{-1}(x)$?

score 724 · Answer 1 · 2020-05-06 05:13:18

724

Views

What is the coefficient of $x^7$ in the Taylor series expansion, around $x=0$ of the function $f(x)=\sin^{-1}(x)$?

Published on 06 May 2020 - 5:13

score 66 · Answer 2 · 2026-04-08 15:01:08

66

Views

Show that $1 + \frac{x}{1!} + \dots + \frac{x^n}{n!} \leq e^x \leq 1 + \frac{x}{1!} + \dots + \frac{x^{n-1}}{(n-1)!} + \frac{e^{a}x^n}{n!}$

Published on 08 Apr 2026 - 15:01

score 243 · Answer 3 · 2026-03-25 07:56:46

243

Views

Richardson Extrapolation on forward differencing formula

Published on 25 Mar 2026 - 7:56

score 69 · Answer 4 · 2020-05-07 04:19:57

Maclaurin series expansion for $\dfrac{1}{2t}\left(1+t-\dfrac{(1-t)^2}{2 \sqrt {t}}\log \left(\dfrac{1+\sqrt{t}}{1-\sqrt{t}}\right)\right)$

score 407 · Answer 5 · 2020-05-07 05:46:43

407

Views

Clarification on Second Order Taylor Theorem for Scalar Fields

Published on 07 May 2020 - 5:46

score 27 · Answer 6 · 2026-03-27 21:18:08

27

Views

Can the radius of convergence be equal to 1 (arctangent function)?

Published on 27 Mar 2026 - 21:18

score 602 · Answer 7 · 2026-03-29 11:48:32

602

Views

Proving: $\frac{1}{2m}\left|\left|\nabla f(x)\right|\right|_{2}^{2}\leq f(x)-f(x^{*})\leq\frac{1}{2M}\left|\left|\nabla f(x)\right|\right|_{2}^{2}$

Published on 29 Mar 2026 - 11:48

score 142 · Answer 8 · 2026-02-23 04:56:31

142

Views

Approximate the integral $\int_0^{0.5}{x^2e^{x^2}}dx$ correct to four decimal places using a Maclaurin series.

Published on 23 Feb 2026 - 4:56

score 200 · Answer 9 · 2026-02-23 04:50:00

200

Views

forward - backward differencing = central differencing

Published on 23 Feb 2026 - 4:50

score 125 · Answer 10 · 2020-05-09 16:52:45

125

Views

When approximating a function using a Taylor series, can your approximation get worse by adding the next term?

Published on 09 May 2020 - 16:52

score 58 · Answer 11 · 2020-05-09 17:03:51

58

Views

Showing that the radius of convergence of a power series is $R=\infty$

Published on 09 May 2020 - 17:03

score 161 · Answer 12 · 2026-03-27 01:46:47

161

Views

Consider the initial value problem $y'=y+x, y(0)=2$. Find the first $4$ terms of the Taylor series.

Published on 27 Mar 2026 - 1:46

score 91 · Answer 13 · 2020-05-09 22:37:44

91

Views

Write f(z) as a power series around zero and identify the radius of convergence $f(z) = \frac{e^z}{z-1}$

Published on 09 May 2020 - 22:37

score 1.2k · Answer 14 · 2020-05-10 22:10:33

1.2k

Views

Taylor Functions for Complex and Real Valued Functions

Published on 10 May 2020 - 22:10

score 30 · Answer 15 · 2020-05-10 22:54:04

30

Views

Bounds of the difference of two Taylor polynomials upto derivatives

Published on 10 May 2020 - 22:54

List Question

What is the coefficient of $x^7$ in the Taylor series expansion, around $x=0$ of the function $f(x)=\sin^{-1}(x)$?

Show that $1 + \frac{x}{1!} + \dots + \frac{x^n}{n!} \leq e^x \leq 1 + \frac{x}{1!} + \dots + \frac{x^{n-1}}{(n-1)!} + \frac{e^{a}x^n}{n!}$

Richardson Extrapolation on forward differencing formula

Maclaurin series expansion for $\dfrac{1}{2t}\left(1+t-\dfrac{(1-t)^2}{2 \sqrt {t}}\log \left(\dfrac{1+\sqrt{t}}{1-\sqrt{t}}\right)\right)$

Clarification on Second Order Taylor Theorem for Scalar Fields

Can the radius of convergence be equal to 1 (arctangent function)?

Proving: $\frac{1}{2m}\left|\left|\nabla f(x)\right|\right|_{2}^{2}\leq f(x)-f(x^{*})\leq\frac{1}{2M}\left|\left|\nabla f(x)\right|\right|_{2}^{2}$

Approximate the integral $\int_0^{0.5}{x^2e^{x^2}}dx$ correct to four decimal places using a Maclaurin series.

forward - backward differencing = central differencing

When approximating a function using a Taylor series, can your approximation get worse by adding the next term?

Showing that the radius of convergence of a power series is $R=\infty$

Consider the initial value problem $y'=y+x, y(0)=2$. Find the first $4$ terms of the Taylor series.

Write f(z) as a power series around zero and identify the radius of convergence $f(z) = \frac{e^z}{z-1}$

Taylor Functions for Complex and Real Valued Functions

Bounds of the difference of two Taylor polynomials upto derivatives

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