List questions from multivariable-calculus

Published on 16 Apr 2026 - 11:02

224

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What will be the Hessian matrix of $(\ln(x+y))^{xy}$ at $(x_0,y_0)=(1,1)$?

Published on 16 Apr 2026 - 7:50

56

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Exercise of continuity of a function of two variables

Published on 17 Apr 2026 - 5:29

33

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$\not\exists$ bijective function $f:\Bbb{R}^n\to A(\subset\Bbb{R}^m~m>n)$such that $f$ and $f^{-1}$ are both differentiable.

Published on 16 Apr 2026 - 19:49

98

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show this $\prod(a^3+b^3+ab)^2\ge (\sum a^2b)^3( \sum ab^2)^3$

Published on 15 Apr 2026 - 6:40

155

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Difficult change of variables: region of integration

Published on 11 Apr 2026 - 9:12

5.3k

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Find the equation of the plane tangent to the surface at a given point

Published on 13 Apr 2026 - 21:31

149

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Limit of determinant/norm

Published on 13 Apr 2026 - 21:04

51

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Isn't a $u$-substitution a map going in the wrong direction?

Published on 15 Apr 2026 - 18:13

1k

Views

Find the maximum of a nonlinear function of two variables

Published on 29 Mar 2026 - 20:38

749

Views

Find the point(s) at the surface such that the tangent plane goes through (3,0,0) and (0,3,0)

Published on 15 Apr 2026 - 5:16

447

Views

Rotation of a curl?

Published on 17 Apr 2026 - 2:12

302

Views

Triple integral between spheres $\iiint \sin (xy) - \sin (xz) + \sin (yz) \,dx \,dy \,dz$

Published on 13 Apr 2026 - 21:31

753

Views

Integral of Laplacian of Compactly Supported Function

Published on 11 Apr 2026 - 0:04

347

Views

Hessian on non-critical points

Published on 13 Apr 2026 - 23:39

List Question

What are the local extreme values of $f(x,y)=x^3+x^2y-y^2-4y$?

What will be the Hessian matrix of $(\ln(x+y))^{xy}$ at $(x_0,y_0)=(1,1)$?

Exercise of continuity of a function of two variables

$\not\exists$ bijective function $f:\Bbb{R}^n\to A(\subset\Bbb{R}^m~m>n)$such that $f$ and $f^{-1}$ are both differentiable.

show this $\prod(a^3+b^3+ab)^2\ge (\sum a^2b)^3( \sum ab^2)^3$

Difficult change of variables: region of integration

Find the equation of the plane tangent to the surface at a given point

Limit of determinant/norm

Isn't a $u$-substitution a map going in the wrong direction?

Find the maximum of a nonlinear function of two variables

Find the point(s) at the surface such that the tangent plane goes through (3,0,0) and (0,3,0)

Rotation of a curl?

Triple integral between spheres $\iiint \sin (xy) - \sin (xz) + \sin (yz) \,dx \,dy \,dz$

Integral of Laplacian of Compactly Supported Function

Hessian on non-critical points

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