Verify that the function

if

and

if

,

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,

doesn't seem definied in

.

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.