# 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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### Triple integral question- two balls in $\mathbb{R}^3$

How can I calculate the volume bounded between the two surfaces: $$x^2+y^2+z^2=1, \quad x^2+(y-1)^2+z^2=1$$ and contains the point $(0,0.5,0)$. When I move to spherical coordinates, I obtain ...
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### tangent to a level surface

Let $F:\mathbb{R}\to \mathbb{R}^n$ be differentiable. Let $f:\mathbb{R}^n \to \mathbb{R}$ be continuously differentiable and such that the composition $g(t)=f(F(t))$ exists. If $F'(t_0)$ is tangent ...
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### Find the limit of the vector function

$lim_{t\to\infty} \Big(te^{-t},\frac{t^3+t}{2t^3-1},tsin(\frac{1}{t})\Big)$ a) $lim_{t\to\infty} te^{-t} = \infty \times 0$ $lim_{t\to\infty} 1e^{-t}+-e^tt = 0+(0\times\infty)$=undefined, and ...
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### Difficulty setting up an iterated integral

I am trying to integrate the function $\frac{1}{\sqrt{2y-y^2}}$ over the region in the first quadrant bounded by $x^2=4-2y$. Given that this region is between bounded by an convex parabola and in the ...
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### Question about terminology of Munkres's Analysis on Manifold text

The definition above are given by Munkres when he defined Euclidean manifold. One question I have about terminology is that when he says " For each $p \in M$, there is an open set $V$ of $M$ ..... ", ...
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### 2nd derivative of xy w/ respect to x?

$$\frac{d^2}{dx^2}xy$$ I know it equals zero but I don't know the in between-steps. I'm using it to prove Newtons Laws work in any frame of reference. So say two guys start from the same point and ...
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### Application of Chain Rule for Paths

I'm a graduate student and I'm currently teaching multivariable calculus. I gave my students a question about a bug traveling along a circle of radius $200$cm in the $xy$-plane. We suppose also that ...