Thread: 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.

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).




Tonio


If not explain why the limit does not exist.

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