1. ## Discontinuity

Define f: R^n \ (0,0,...0) -> R by f(x)=e^(-1/||x||^2) . Explain why the origin is a point of discontinuity. Can the discontinuity be removable? If so, determine
lim(x->0) f(x). If not explain why the limit does not exist.

2. Originally Posted by poorna
Define f: R^n \ (0,0,...0) -> R by f(x)=e^(-1/||x||^2) . Explain why the origin is a point of discontinuity.

Because the function isn't defined there

Can the discontinuity be removable? If so, determine
lim(x->0) f(x).

$\lim\limits_{x\to 0}e^{-1/||x||^2}=0$

Tonio

If not explain why the limit does not exist.
.