Suppose $\displaystyle \lim_{x \to 4} \frac{f(x)}{x^2} = 1$. Find the following limits.

(a) $\displaystyle \lim_{x \to 4} f(x) =$ .

(b) $\displaystyle \lim_{x \to 4} \frac{\sqrt{x} f(x)}{x^2-3} =$ .