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Proof of Continuity – A split function with exponential functions and a parameter – Exercise 6591

Exercise

Given the function

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

a> 0 is a parameter. For what values of the parameter the function is continuous?

Final Answer


a=\frac{1}{e}

Solution

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