Question

Clarification on the use of dot product in the formula for a plane's distance to origin

score 1.8k · Answer 1 · 2026-04-14 23:20:56

1.8k

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Clarification on the use of dot product in the formula for a plane's distance to origin

Published on 14 Apr 2026 - 23:20

score 63 · Answer 2 · 2026-04-15 10:47:17

63

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Multidimensional level sets

Published on 15 Apr 2026 - 10:47

score 61 · Answer 3 · 2026-04-16 15:10:20

61

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Finding the hessian matrix of $f(x) = g^t(x)g(x)$

Published on 16 Apr 2026 - 15:10

score 34 · Answer 4 · 2026-04-16 14:23:34

34

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Prove angles of $(\vec r), (\vec v),(\vec a)$ are constant in this trajectory

Published on 16 Apr 2026 - 14:23

score 169 · Answer 5 · 2026-04-11 00:45:06

169

Views

Computation of multiple improper integral.

Published on 11 Apr 2026 - 0:45

score 57 · Answer 6 · 2026-03-25 11:21:46

57

Views

If $\varphi(x,y)=(x,F(x,y))$ invertible, why it's inverse is of the form $\psi(u,v)=(u, G(u,v))$?

Published on 25 Mar 2026 - 11:21

score 33 · Answer 7 · 2026-04-10 16:44:58

33

Views

Compose a tensor and matrix

Published on 10 Apr 2026 - 16:44

score 767 · Answer 8 · 2026-04-15 11:49:34

767

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$u$ is harmonic in $\mathbb{R}^N$ then if $T$ is an orthogonal transformation, $u\circ T$ is harmonic in $\mathbb{R}^N$

Published on 15 Apr 2026 - 11:49

score 116 · Answer 9 · 2026-05-04 14:55:36

116

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If $f(x)=\langle x,a\rangle e^{-\langle x, x\rangle} \ \forall x, a \in \Bbb{R}^{n}$, then prove that $f$ is of class $C^{1}$ and compute $f'(x)$

Published on 04 May 2026 - 14:55

score 115 · Answer 10 · 2026-05-04 14:55:36

115

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If $f(x,y)=e^{x-y}-x-y-1,\forall\;(x,y)\in\Bbb{R}^2$, then $\exists\;\alpha>0$ and $\varphi:\,]-\alpha,\alpha[\to\Bbb{R}$ of class $\Bbb{C}^{\infty}$

Published on 04 May 2026 - 14:55

score 116 · Answer 11 · 2026-05-04 14:55:36

116

Views

Prove that $\Vert f(x) -f(y)\Vert\geq (1-k)\Vert x-y\Vert,\;\text{and}\;\Vert f'(x)h\Vert\geq (1-k)\Vert h\Vert,\;\forall\,x,y,h\in\Bbb{R^n}$

Published on 04 May 2026 - 14:55

score 67 · Answer 12 · 2026-04-09 17:45:30

67

Views

Changing expectations into probability.

Published on 09 Apr 2026 - 17:45

score 69 · Answer 13 · 2026-04-16 08:53:39

69

Views

Let $f\colon \mathbb R^2 \to \mathbb R^2$ differentiable. Given $Df(0,0)$, show $\lim\limits_{(x,y)\to (0,0)} \frac{||f(x,y)-f(0,0)||}{||(x,y)||}=3$

Published on 16 Apr 2026 - 8:53

score 74 · Answer 14 · 2026-04-10 01:19:21

74

Views

integration with angles in spherical coordinates

Published on 10 Apr 2026 - 1:19

score 812 · Answer 15 · 2026-04-15 04:38:35

812

Views

Surface Integral formed by Paraboloid of revolution and Cylinder

Published on 15 Apr 2026 - 4:38

List Question

Clarification on the use of dot product in the formula for a plane's distance to origin

Multidimensional level sets

Finding the hessian matrix of $f(x) = g^t(x)g(x)$

Prove angles of $(\vec r), (\vec v),(\vec a)$ are constant in this trajectory

Computation of multiple improper integral.

If $\varphi(x,y)=(x,F(x,y))$ invertible, why it's inverse is of the form $\psi(u,v)=(u, G(u,v))$?

Compose a tensor and matrix

$u$ is harmonic in $\mathbb{R}^N$ then if $T$ is an orthogonal transformation, $u\circ T$ is harmonic in $\mathbb{R}^N$

If $f(x)=\langle x,a\rangle e^{-\langle x, x\rangle} \ \forall x, a \in \Bbb{R}^{n}$, then prove that $f$ is of class $C^{1}$ and compute $f'(x)$

If $f(x,y)=e^{x-y}-x-y-1,\forall\;(x,y)\in\Bbb{R}^2$, then $\exists\;\alpha>0$ and $\varphi:\,]-\alpha,\alpha[\to\Bbb{R}$ of class $\Bbb{C}^{\infty}$

Prove that $\Vert f(x) -f(y)\Vert\geq (1-k)\Vert x-y\Vert,\;\text{and}\;\Vert f'(x)h\Vert\geq (1-k)\Vert h\Vert,\;\forall\,x,y,h\in\Bbb{R^n}$

Changing expectations into probability.

Let $f\colon \mathbb R^2 \to \mathbb R^2$ differentiable. Given $Df(0,0)$, show $\lim\limits_{(x,y)\to (0,0)} \frac{||f(x,y)-f(0,0)||}{||(x,y)||}=3$

integration with angles in spherical coordinates

Surface Integral formed by Paraboloid of revolution and Cylinder

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