Question

Are these two derivative calculations correct for inverse hyperbolic functions?

score 41 · Answer 1 · 2026-04-16 13:06:06

41

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Are these two derivative calculations correct for inverse hyperbolic functions?

Published on 16 Apr 2026 - 13:06

score 63 · Answer 2 · 2026-04-05 15:55:06

63

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Integrating extended function

Published on 05 Apr 2026 - 15:55

score 628 · Answer 3 · 2026-03-26 12:26:55

628

Views

Let $f : \mathbb{R}^n\to \mathbb{R}^n$ be given by the equation $f(x) = ||x||^2·x$. Show that $f$ is of class $C^{\infty}$ and that $f$

Published on 26 Mar 2026 - 12:26

score 75 · Answer 4 · 2026-04-23 07:31:01

75

Views

Extremum of a function

Published on 23 Apr 2026 - 7:31

score 35 · Answer 5 · 2026-04-16 18:59:19

35

Views

Find a way of computing $x_{20}$ accurately, perhaps by replacing the integrand by a truncated Taylor series. After computing $x_{20}$ to full

Published on 16 Apr 2026 - 18:59

score 188 · Answer 6 · 2026-04-16 22:43:37

188

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Prove that $\int{\frac{x^2}{(x^2 + a^2)^n}}dx = \int{\frac{1}{(x^2 + a^2)^n}}dx - a^2\int{\frac{1}{(x^2 + a^2)^{n+1}}}dx$

Published on 16 Apr 2026 - 22:43

score 720 · Answer 7 · 2026-04-15 06:58:54

720

Views

Mean and Variance of a Random Variable with a Given PDF

Published on 15 Apr 2026 - 6:58

score 78 · Answer 8 · 2026-04-10 14:32:20

78

Views

Problem to define a parabola with two tangents

Published on 10 Apr 2026 - 14:32

score 406 · Answer 9 · 2026-04-18 11:10:13

406

Views

Change of variable and divergence

Published on 18 Apr 2026 - 11:10

score 38 · Answer 10 · 2026-04-13 22:16:28

38

Views

Area Between 2 Curves Integration Help

Published on 13 Apr 2026 - 22:16

score 38 · Answer 11 · 2026-04-11 23:54:25

38

Views

Finding derivative of a product

Published on 11 Apr 2026 - 23:54

score 324 · Answer 12 · 2026-04-07 09:45:09

324

Views

A limit question of 3-variable-functions. $\lim\limits_{ (x,y,z) \to (0,0,0)} \frac {xyz^2}{x^2+y^4+z^6}$

Published on 07 Apr 2026 - 9:45

score 1.4k · Answer 13 · 2026-04-13 22:34:14

1.4k

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What happens when you apply L'Hospital's rule and still get infinity over infinity?

Published on 13 Apr 2026 - 22:34

score 65 · Answer 14 · 2026-04-16 02:30:36

$(\sum_{i=1}^{\infty} |x_i|^\beta)^{\frac{\alpha}{\beta}} \leq \sum_{i=1}^{\infty} |x_i|^\alpha$ where $x_i\in \mathbb{R}$ and $0<\alpha<\beta$.

score 450 · Answer 15 · 2026-04-16 05:15:56

450

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How to prove that $f(x,y) =(x^2-y^2)e^{-x^2-y^2} $ attains its maximum and its minimum.

Published on 16 Apr 2026 - 5:15

List Question

Are these two derivative calculations correct for inverse hyperbolic functions?

Integrating extended function

Let $f : \mathbb{R}^n\to \mathbb{R}^n$ be given by the equation $f(x) = ||x||^2·x$. Show that $f$ is of class $C^{\infty}$ and that $f$

Extremum of a function

Find a way of computing $x_{20}$ accurately, perhaps by replacing the integrand by a truncated Taylor series. After computing $x_{20}$ to full

Prove that $\int{\frac{x^2}{(x^2 + a^2)^n}}dx = \int{\frac{1}{(x^2 + a^2)^n}}dx - a^2\int{\frac{1}{(x^2 + a^2)^{n+1}}}dx$

Mean and Variance of a Random Variable with a Given PDF

Problem to define a parabola with two tangents

Change of variable and divergence

Area Between 2 Curves Integration Help

Finding derivative of a product

A limit question of 3-variable-functions. $\lim\limits_{ (x,y,z) \to (0,0,0)} \frac {xyz^2}{x^2+y^4+z^6}$

What happens when you apply L'Hospital's rule and still get infinity over infinity?

$(\sum_{i=1}^{\infty} |x_i|^\beta)^{\frac{\alpha}{\beta}} \leq \sum_{i=1}^{\infty} |x_i|^\alpha$ where $x_i\in \mathbb{R}$ and $0<\alpha<\beta$.

How to prove that $f(x,y) =(x^2-y^2)e^{-x^2-y^2} $ attains its maximum and its minimum.

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