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.
Thanks a lot mathstud28. I did the calculation of the limit on my draft too fast... I looked only at the denominator and since it tends to 0 I thought the limit would be undefinied but as you say, the exponential tends to 0 faster than any polynomial and so the limit is well defined. Ok for the rest, I get it.