# 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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### $\int_{\partial B_1(0)} \omega f(\omega r) d\omega = 0$ for every $r \ge 0$ implies $\nabla f(0) = 0$?

Let $f:\mathbb R^N \to \mathbb R$ be a smooth function and assume that $$\int_{\partial B_1(0)} \omega f(\omega r) d\omega = 0$$ for every $r \ge 0$, where $\partial B_1(0)$ denotes the sphere of unit ...
Theorem: let $X:I\to \mathbb R^n$ be a curve whose speed $v(t)$ is $>0$ for all $t$ in the interval of definition, Let $\text{ (1)}$ $$s(t)=\int_a^tv(u)\,du \text{ (2)}$$ and $t=f(s)$ be the ...