Proof of Continuity – A split function with a quotient of functions and parameters – Exercise 5867


Given the function

f(x) = \begin{cases} \frac{x^2-8x-9}{3-\sqrt{x}}, &\quad x>9\\ ax+b-6, &\quad 0\leq x\leq 9\\ e^{\frac{1}{x}}, &\quad x<0\\ \end{cases}

a and b are parameters. For which values of the parameters the function is continuous?

Final Answer

a=-\frac{20}{3}, b=6


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