Answer
(a) 16
(b) $\frac{1}{4}$
(c) 12
Work Step by Step
Using the basic limit laws, we have
(a) $\lim\limits_{x \to 6}f(x)^{2}=(\lim\limits_{x \to 6}f(x))^{2}=4^{2}=16$
(b) $\lim\limits_{x \to 6}\frac{1}{f(x)}=\frac{1}{\lim\limits_{x \to 6}f(x)}=\frac{1}{4}$
(c) $\lim\limits_{x \to 6} x\sqrt {f(x)}=(\lim\limits_{x \to 6}x)(\sqrt {\lim\limits_{x\to 6}f(x)})$$=6\times\sqrt 4=12$
