## Calculus with Applications (10th Edition)

see: Rules for Limits Let $a, A$, and $B$ be real numbers, and let $f$ and $g$ be functions such that $\displaystyle \lim_{x\rightarrow a}f(x)=A$ and $\displaystyle \lim_{x\rightarrow a}g(x)=B$. 8. For any real number $b>0,$ $\displaystyle \lim_{x\rightarrow a}b^{f(x)}=b^{[\lim_{x\rightarrow a}f(x)]}=b^{A}$. --------------- $\displaystyle \lim_{x\rightarrow 4}2^{f(x)}=2^{\lim_{x\rightarrow 4}f(x)}$ $=2^{9}$ $=512$