Question

suppose lim[x:4,f(x)=4] and lim[x:4,g(x)= -2], find,
lim[x:4,g(x)/f(x)-1]

Answer 1

$$\begin{align*}
\lim \limits_{x\to 4} \frac{g(x)}{f(x)-1}&=\frac{\lim \limits_{x\to 4} g(x)}{\lim \limits_{x\to 4}[ f(x)-1]}\\
&=\frac{\lim \limits_{x\to 4} g(x)}{\lim \limits_{x\to 4}f(x)-1}
\end{align*}$$