List questions from multivariable-calculus

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Proving integral inequality for all $f\in H^1(D)$

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Taking the derivative of a quadratic form

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Let $f:\mathbb{R}^2\to \mathbb{R}$ be of class $C^1$, with $f(2,-1)=-1$. Set $G(x,y,u)=f(x,y)+u^2, H(x,y,u)= ux+3y^3+u^3$.

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Compute $\iint_D e^{(x+y)^2} \ dxdy.$

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What is the value of $\lim_{(x,y,z)\rightarrow(0,0,0)}\log(\frac{x}{yz})$?

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What is the correct answer1?

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Transform 2-dimensional integral to 1-dimensional one

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Every Point on a Surface is a Boundary point or a Interior Point

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$C^r$ map between a manifold and $\mathbb{R}$

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One question regarding the jacobian of a function

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Bivariate probability help

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How to integrate this in a double integral problem?

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Integral of regions

Published on 07 Apr 2026 - 14:46

List Question

Using Clairaut's Theorem to show $\beta=yzdx -xzdy +xydz$ is not a differential of a function?

Proving integral inequality for all $f\in H^1(D)$

Taking the derivative of a quadratic form

Let $f:\mathbb{R}^2\to \mathbb{R}$ be of class $C^1$, with $f(2,-1)=-1$. Set $G(x,y,u)=f(x,y)+u^2, H(x,y,u)= ux+3y^3+u^3$.

Compute $\iint_D e^{(x+y)^2} \ dxdy.$

What is the value of $\lim_{(x,y,z)\rightarrow(0,0,0)}\log(\frac{x}{yz})$?

What is the correct answer1?

Transform 2-dimensional integral to 1-dimensional one

Prize pool distribution

Every Point on a Surface is a Boundary point or a Interior Point

$C^r$ map between a manifold and $\mathbb{R}$

One question regarding the jacobian of a function

Bivariate probability help

How to integrate this in a double integral problem?

Integral of regions

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