## Calculus: Early Transcendentals (2nd Edition)

$\lim\limits_{x \to 1}{\frac{f(x)}{h(x)}}=4$
$\lim\limits_{x \to 1}{\frac{f(x)}{h(x)}}$ Quotient: because $\lim\limits_{x \to 1}{h(x)} = 2\ne0$ $\lim\limits_{x \to 1}{\frac{f(x)}{h(x)}}=\frac{\lim\limits_{x \to 1}{f(x)}}{\lim\limits_{x \to 1}{h(x)}}$ We know that $\lim\limits_{x \to 1}{f(x)} = 8$ $\lim\limits_{x \to 1}{\frac{f(x)}{h(x)}}=\frac{\lim\limits_{x \to 1}{f(x)}}{\lim\limits_{x \to 1}{h(x)}}=\frac{8}{2}=4$ So $\lim\limits_{x \to 1}{(4f(x))}=4\lim\limits_{x \to 1}{f(x)} = 4\times8=32$