List questions from multivariable-calculus

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Solution verification post : Problem $12.1$, Mathematical Analysis, Apostol

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Help with a Problem Involving the Properties of Directional Derivatives

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Solution verification post : Problem $12.2$, Mathematical Analysis, Apostol

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show $\lim\limits_{(x,y)\to(0,0)}\frac{|x|^a|y|^b}{|x|^c+|y|^d}$ exists and equals $0$?

Published on 16 Apr 2026 - 13:39

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To prove that $f(z) = constant$ if $f'(z) = 0$, why is it necessary to prove that $u$ and $v$ are constant for all paths?

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Is the nonnegative orthant isometric to itself under orthogonal mapping?

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Inequality with $\frac{x^2+y^2+z^2+w}{(x+y+z)^3}$

Published on 15 Apr 2026 - 16:27

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How to find the closed path such that $\int\limits_\Gamma F\cdot dl\ne0$

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Iterations of a multivariable function

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Interpretation of $\int_C \vec A.d\vec r=\int^{(c,d)}_{(a,b)}dN=N(c,d)-N(a-b)$?

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Is it possible to integrate this function without using spherical coordinates?

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Is there a vertical line test correlate in 3 space?

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Find $\frac{\partial f}{\partial x}$ where $f=h(x+y,y^2,x+z)$

Published on 15 Apr 2026 - 12:10

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How to switch to polar coordinates with Gaussian Integral?

Published on 09 Apr 2026 - 21:55

List Question

Showing continuity of $xy$ at all points

Solution verification post : Problem $12.1$, Mathematical Analysis, Apostol

Help with a Problem Involving the Properties of Directional Derivatives

Solution verification post : Problem $12.2$, Mathematical Analysis, Apostol

show $\lim\limits_{(x,y)\to(0,0)}\frac{|x|^a|y|^b}{|x|^c+|y|^d}$ exists and equals $0$?

To prove that $f(z) = constant$ if $f'(z) = 0$, why is it necessary to prove that $u$ and $v$ are constant for all paths?

Is the nonnegative orthant isometric to itself under orthogonal mapping?

Inequality with $\frac{x^2+y^2+z^2+w}{(x+y+z)^3}$

How to find the closed path such that $\int\limits_\Gamma F\cdot dl\ne0$

Iterations of a multivariable function

Interpretation of $\int_C \vec A.d\vec r=\int^{(c,d)}_{(a,b)}dN=N(c,d)-N(a-b)$?

Is it possible to integrate this function without using spherical coordinates?

Is there a vertical line test correlate in 3 space?

Find $\frac{\partial f}{\partial x}$ where $f=h(x+y,y^2,x+z)$

How to switch to polar coordinates with Gaussian Integral?

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