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**arbolis** Verify that the function $\displaystyle f_a(x)=0$ if $\displaystyle |x|\geq |a|$ and $\displaystyle f_a (x)= exp \{ \frac{-1}{x+a}+ \frac{-1}{x-a} \}$ if $\displaystyle |x|< |a|$, $\displaystyle x \in \mathbb{R}$ is infinitely many times differentiable and has a compact support.

I have this exercise in an electromagnetism course and I never heard about compact support before. I've been told that if I can bound the function inside a sphere of a finite radius, then the function is of compact support. But reading the wikipedia article on it, I'm more lost than before.

Furthermore if I take the definition of a limit of a function, $\displaystyle f'_a(x)$ doesn't seem definied in $\displaystyle a$.

It might be some kind of distribution function and I never took any course on the subject so I'm really lost.

Any help is appreciated.