Answer
a. $0$
b. No value of $k$ will make the function continuous.
Work Step by Step
a. Note that $\lim_{x \to -3^+} f(x) = f(-3) = 0$. For $f(x)$ to be continuous, $\lim_{x \to -3^-} f(x) = 0$. Thus, $\lim_{x \to -3^-} f(x) = \frac{k}{(-3)^2} = 0$. Therefore $k=0$.
b. Note that $\lim_{x \to 0^+} f(x) = f(0) = 9$. For $f(x)$ to be continuous, $\lim_{x \to 0^-} f(x) = 9$. However, $\lim_{x \to 0^-} f(x) = \infty$ for all values of $k$. Thus, there does not exist a value of $k$ which will make the function continuous.
