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.
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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). $\displaystyle \lim\limits_{x\to 0}e^{-1/||x||^2}=0$ Tonio If not explain why the limit does not exist. .
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