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# Continuity test

A function $$f : \mathbb{R} \rightarrow \mathbb{R}$$ is defined by

$$f(x) = e^{-\frac{1}{x}}$$ for $$x>0$$, and $$0$$ for $$x \leq 0$$.

Then is $$f$$ continuous and differentiable? Is $$f'$$ continuous?

Note by Paramjit Singh
3 years, 8 months ago