# Questions tagged [multivariable-calculus]

Use this tag for questions about differential and integral calculus with more than one independent variable. Some related tags are (differential-geometry), (real-analysis), and (differential-equations).

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### is transposed vector times transposed vector possible?

I was wondering if it was indeed possible to perform a transposed vector multiplication with another transposed vector. And if so how I'm supposed to do so. Background: From https://en.wikipedia.org/...
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### Flux through surface of revolution

I'm trying to solve the following problem Let $C$ be the curve in the $xy$ plane given in polar coordinates by $r = 2-\sin(\theta),\ 0 \leq \theta \leq \pi$ and let $S$ be the surface given by ...
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### How to know which double integral corresponds to which graph

This is the question This is what I did to sketch the regions of integration for (A), (B), and (C) So, for (a) The area of the triangle in the xy-plane corresponds to C (b) The area of a region in ...
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I am trying to solve a problem from my homework and I am one step away of getting it done. Let $a< b$ two real numbers and consider the multiple integral: $$I = \int_{a}^{b}dx_{1}\int_{a}^{x_{1}}... 7 votes 1 answer 33 views ### Partial derivative of a function their variables depend on each other if z=F\left(x,y\right) and y=\phi \left(x\right) Then is it correct to say that z is just a function of a single variable which is x ? and if we try to compute \frac{\partial z}{\... 1 vote 1 answer 32 views ### Where is my mistake in showing \nabla \mathbf{a}^{T}\mathbf{x}=a_{1}+a_{2}+\cdots+a_{n}? Let f:=\mathbf{a}^{T}\mathbf{x}. The claim that:$$\nabla f=\nabla\mathbf{a}^{T}\mathbf{x}=\|\mathbf{a}\|_{1}=a_{1}+a_{2}+\cdots+a_{n}\tag{1}$$is false where in fact the true answer is \mathbf{a}^{... 0 votes 1 answer 64 views ### How to transform triple integral \iiint_\Omega \sqrt{1- \frac{x^2}{a^2}- \frac{y^2}{b^2} - \frac{z^2}{c^2} }\ dx dy dz I have stumbled across this triple integral$$\iiint_\Omega \sqrt{1- \frac{x^2}{a^2}- \frac{y^2}{b^2} - \frac{z^2}{c^2} }\ dx dy dz$$where$$\Omega =\left\{(x,y,z)\in{\cal{R}}^3\ \bigg| \ \frac{x^2}{...
While reading a text in multivariable calculus , a following definition of higher order derivatives in normed linear spaces is given like this : If $U\subset E$ is open in some normed linear space $E$...