Question

Does $\lim_{(a, b) \to (0, 0)} \sqrt{\frac{a^2b^2}{a^2 + b^2}} = 0$?

score 77 · Answer 1 · 2026-04-16 19:57:03

Does $\lim_{(a, b) \to (0, 0)} \sqrt{\frac{a^2b^2}{a^2 + b^2}} = 0$?

Published on 16 Apr 2026 - 19:57

score 25 · Answer 2 · 2026-04-17 05:36:25

Find the boundary of $\mathcal{D}_n:=\left\{(x_1,\dots,x_n,y)\, \big|\, 0\leq x_i\leq y\, ,\forall i=1,\dots,n,\, y\in[0,1]\right\}\, .$

score 26 · Answer 3 · 2026-04-12 06:27:19

26

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Creating a circle equation that has a specific slope at a specific point

Published on 12 Apr 2026 - 6:27

score 1.1k · Answer 4 · 2026-04-09 03:29:52

1.1k

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How to evaluate this nonelementary integral?

Published on 09 Apr 2026 - 3:29

score 1k · Answer 5 · 2026-04-14 20:47:44

1k

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Moment of inertia of a solid right circular cone

Published on 14 Apr 2026 - 20:47

score 47 · Answer 6 · 2026-04-13 18:17:14

47

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Use chain rule to find expression for $\frac{\partial f}{\partial t}$

Published on 13 Apr 2026 - 18:17

score 403 · Answer 7 · 2026-04-14 09:32:08

403

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Calculate the double integral over the region $xy^3e^{x^2y^2} \space R[1,3] X [1,2]$

Published on 14 Apr 2026 - 9:32

score 103 · Answer 8 · 2026-04-17 11:49:30

Continuity and existence of directional derivatives at all directions of a $f:\mathbb{R}^{2} \to \mathbb{R}$ given by $f(x,y)=\frac{2x^2y}{x^2+y^2}$

score 106 · Answer 9 · 2026-05-11 00:43:04

106

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Is there a systematic way to construct functions with prescribed local extrema?

Published on 11 May 2026 - 0:43

score 496 · Answer 10 · 2026-04-09 02:59:31

496

Views

Multidimensionally Lipschitz continuous iff Lipschitz continuous in every coordinate

Published on 09 Apr 2026 - 2:59

score 94 · Answer 11 · 2026-04-11 12:44:07

94

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Evaluating the limit of multivariable function

Published on 11 Apr 2026 - 12:44

score 32 · Answer 12 · 2026-04-16 00:01:05

32

Views

Does $f(x,y,z)=(1 + |x|+|y|) \cosh(|x|-|y| + z^2)$ have extrema other than at the origin?

Published on 16 Apr 2026 - 0:01

score 38 · Answer 13 · 2026-04-17 02:22:34

38

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$\int_Df(x+y)x^my^n d\lambda_2(x,y)^T=\frac{m!n!}{(m+n+1)!}\int_{0}^{1}f(t)t^{m+n+1}dt$

Published on 17 Apr 2026 - 2:22

score 119 · Answer 14 · 2026-04-17 15:52:03

119

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Notation: limit in two variables

Published on 17 Apr 2026 - 15:52

score 42 · Answer 15 · 2026-04-16 22:39:46

42

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Derivative of $f = {\rm tr} \left[ U^T \; {\rm unvec} \left( B \ {\rm vec}(X) \right) \right]$ w.r.t. $X$?

Published on 16 Apr 2026 - 22:39

List Question

Does $\lim_{(a, b) \to (0, 0)} \sqrt{\frac{a^2b^2}{a^2 + b^2}} = 0$?

Find the boundary of $\mathcal{D}_n:=\left\{(x_1,\dots,x_n,y)\, \big|\, 0\leq x_i\leq y\, ,\forall i=1,\dots,n,\, y\in[0,1]\right\}\, .$

Creating a circle equation that has a specific slope at a specific point

How to evaluate this nonelementary integral?

Moment of inertia of a solid right circular cone

Use chain rule to find expression for $\frac{\partial f}{\partial t}$

Calculate the double integral over the region $xy^3e^{x^2y^2} \space R[1,3] X [1,2]$

Continuity and existence of directional derivatives at all directions of a $f:\mathbb{R}^{2} \to \mathbb{R}$ given by $f(x,y)=\frac{2x^2y}{x^2+y^2}$

Is there a systematic way to construct functions with prescribed local extrema?

Multidimensionally Lipschitz continuous iff Lipschitz continuous in every coordinate

Evaluating the limit of multivariable function

Does $f(x,y,z)=(1 + |x|+|y|) \cosh(|x|-|y| + z^2)$ have extrema other than at the origin?

$\int_Df(x+y)x^my^n d\lambda_2(x,y)^T=\frac{m!n!}{(m+n+1)!}\int_{0}^{1}f(t)t^{m+n+1}dt$

Notation: limit in two variables

Derivative of $f = {\rm tr} \left[ U^T \; {\rm unvec} \left( B \ {\rm vec}(X) \right) \right]$ w.r.t. $X$?

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