Proof of Continuity – A split function with exponential and rational functions – Exercise 6245


Given the function

f(x) = \begin{cases} \frac{e^x+e^{-x}}{2}, &\quad x>0\\ \frac{1}{1+x^2}, &\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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