# Tagged Questions

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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### $x^2+4xy-2xz-5y^2+6yz-3z^2\leq 0$ $\forall (x,y,z)\in\mathbb{R}^3$

I was thinking to check that the maximum is attached at a negative value, the function $f(x,y,z)=x^2+4xy-2xz-5y^2+6yz-3z^2$ is concave and so the local maximum is a global maximum, but how do I check ...
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### Using higher order derivatives

I am currently learning about the general Notion of Differentiability. I came across some difficulties when working with higher order derivatives and I am hoping for confirmation or comments on some ...
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### For an orientable surface S and a fixed vector v, prove that…

Prove that $$2\iint_S v\cdot n dS = \int_{\partial S}(v\times r) dS$$ where $r=(x,y,z)$ and $n$ is the unit normal vector for $S$.
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### Derivative of function defined as Integral

I have to find all partial derivatives of: $$f(x,y,z) = \int_{\cos x + \sin y}^{z} e^{tz} dt$$ I easily get confused with all this variables, but the idea is to use The Fundamental Theorem of ...
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### Find the absolute extrema of the function over the region R

Find the absolute extrema of the function over the region R where $f(x,y)=x^2+xy, R=\{(x,y)|\;|x|\leq2,|y|\leq1\}$, Here find we going find $f_x=2x+y=0, f_y=x=0 \Rightarrow (x,y)=(0,0)$ is i am ...
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### Techniques for finding functions with known values and derivatives at two points

I want to find a function $\gamma(t) = (x(t),y(t))$ such that for two values of $t$, we have $\gamma'(t)$ and $\gamma(t)$ have some value, and at no point does the curvature ever exceed $r$. What ...
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### Evaluating $\int_0^1\int_0^1 e^{\max\{x^2,y^2\}\,}\mathrm dx\,\mathrm dy$

The integral again for convenience is $$I=\int_0^1\int_0^1 e^{\max\{x^2,y^2\}}\,\mathrm dx\,\mathrm dy$$ My thoughts: Ignoring for a moment that the region is a rectangle, I hoped moving to polar ...
I'm trying to solve the triple integral of $3x^2 + 3y^2 + 3z^2$ in spherical coordinates, with rho from 1 to 2, theta from 0 to 2$\pi$, and $\phi$ from 0 to $\pi /4$. Here's how I'm solving it: First ...