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Continuity by Definition – Classify type of discontinuity – Exercise 831

Exercise

Given the function

f(x) = \begin{cases} \frac{\ln(3x+7)-\ln(5x+e)}{x^2}, &\quad x>0\\ -10+x^3, &\quad x \leq 0\\ \end{cases}

Is it continuous?

Final Answer

No. The point

x=0

  is an essential discontinuity point

Solution

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