Proof of Continuity – A split function with a function to the power of a function – Exercise 6236


Given the function

f(x) = \begin{cases} {(1+x)}^{\frac{1}{x}}, &\quad x>0\\ e-x, &\quad x < 0\\ \end{cases}

Is it continuous at point x = 0? If not, what kind of discontinuity do you get?

Final Answer

No, there is a removable discontinuity


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