Proof of Continuity – A split function with ln and a third root – Exercise 6240


Given the function

f(x) = \begin{cases} \frac{\ln(1+x)}{x}, &\quad x>0\\ \sqrt[3]{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 jump discontinuity


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