Question

Taylor series of $f(x)=\sqrt{1+x^4}$

score 95 · Answer 1 · 2026-04-17 11:16:06

Taylor series of $f(x)=\sqrt{1+x^4}$

Published on 17 Apr 2026 - 11:16

score 38 · Answer 2 · 2026-04-14 21:36:23

Calculus problem dealing with integrals and derivatives as well as position function$= s(t)$, velocity function$= v(t)$, and acceleration$= a(t)$

score 789 · Answer 3 · 2026-05-10 11:48:17

789

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Is a continuously differentiable bi-Lipschitz map on $\mathbf R^d$ a $C^1$-diffeomorphism?

Published on 10 May 2026 - 11:48

score 228 · Answer 4 · 2026-04-18 15:25:53

228

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Computing $f(x) + f\left(\frac{1}{x}\right)$ where $f(x)=\int_{1}^{x}\frac{ \log(t)}{1+t}\,\mathrm{d}t$

Published on 18 Apr 2026 - 15:25

score 97 · Answer 5 · 2026-05-10 16:59:30

97

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Rational result, how? $\int_{1}^{2}{\mathrm dx\over e^x\ln(x+1)}={27\over 100}$

Published on 10 May 2026 - 16:59

score 80 · Answer 6 · 2026-04-12 20:14:50

80

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Question about evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$ (detail)

Published on 12 Apr 2026 - 20:14

score 74 · Answer 7 · 2026-05-10 16:14:28

74

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Does this hold:$\lim_{n \to \infty}{\ln n\over e^n}\int_{0}^{n}{\sinh{x}\over \ln(1+x)}\mathrm dx={1\over 2}$

Published on 10 May 2026 - 16:14

score 75 · Answer 8 · 2026-04-17 10:14:05

75

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Convergence of the series $1-1/2-1/2,...$

Published on 17 Apr 2026 - 10:14

score 1k · Answer 9 · 2026-04-12 09:41:38

1k

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Using Taylor expansion to derive error formula for midpoint rule

Published on 12 Apr 2026 - 9:41

score 173 · Answer 10 · 2026-04-15 20:24:14

173

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Calculate the distance in $C[0,1]$ from the function $x(t) = t^2$ to the linear hull of the functions $y(t) = t$ and $z(t) = \sin t.$

Published on 15 Apr 2026 - 20:24

score 64 · Answer 11 · 2026-04-12 07:30:11

64

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Convergence of smooth surfaces in $\mathbb{R}^3$

Published on 12 Apr 2026 - 7:30

score 2.1k · Answer 12 · 2026-04-23 11:23:15

2.1k

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Proving $ \lim_{x\to\infty}\frac{\sqrt x\cos(x-x^2)}{x+1} = 0. $

Published on 23 Apr 2026 - 11:23

score 257 · Answer 13 · 2026-05-10 18:59:43

257

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$y''$ in terms of $y$ if $y=\cos^{-1}x$

Published on 10 May 2026 - 18:59

score 617 · Answer 14 · 2026-05-11 03:14:22

617

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The Intergral of $\sin^4x$ without using reduction formula

Published on 11 May 2026 - 3:14

score 1.4k · Answer 15 · 2026-04-17 13:01:03

1.4k

Views

How to find local extrema when Hessian is $0$?

Published on 17 Apr 2026 - 13:01

List Question

Taylor series of $f(x)=\sqrt{1+x^4}$

Calculus problem dealing with integrals and derivatives as well as position function$= s(t)$, velocity function$= v(t)$, and acceleration$= a(t)$

Is a continuously differentiable bi-Lipschitz map on $\mathbf R^d$ a $C^1$-diffeomorphism?

Computing $f(x) + f\left(\frac{1}{x}\right)$ where $f(x)=\int_{1}^{x}\frac{ \log(t)}{1+t}\,\mathrm{d}t$

Rational result, how? $\int_{1}^{2}{\mathrm dx\over e^x\ln(x+1)}={27\over 100}$

Question about evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$ (detail)

Does this hold:$\lim_{n \to \infty}{\ln n\over e^n}\int_{0}^{n}{\sinh{x}\over \ln(1+x)}\mathrm dx={1\over 2}$

Convergence of the series $1-1/2-1/2,...$

Using Taylor expansion to derive error formula for midpoint rule

Calculate the distance in $C[0,1]$ from the function $x(t) = t^2$ to the linear hull of the functions $y(t) = t$ and $z(t) = \sin t.$

Convergence of smooth surfaces in $\mathbb{R}^3$

Proving $ \lim_{x\to\infty}\frac{\sqrt x\cos(x-x^2)}{x+1} = 0. $

$y''$ in terms of $y$ if $y=\cos^{-1}x$

The Intergral of $\sin^4x$ without using reduction formula

How to find local extrema when Hessian is $0$?

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