let lim f(x)=2. use the limit rules to find the limit given below. x→4 lim 3^f(x) x→4 lim 3^f(x)=□ x→4…
let lim f(x)=2. use the limit rules to find the limit given below. x→4 lim 3^f(x) x→4 lim 3^f(x)=□ x→4 (simplify your answer.)
Answer
Explanation:
Step1: Recall limit - constant - function rule
If $\lim_{x\rightarrow a}f(x) = L$ and $c$ is a constant, then $\lim_{x\rightarrow a}c^{f(x)}=c^{\lim_{x\rightarrow a}f(x)}$. Here $c = 3$, $a = 4$ and $\lim_{x\rightarrow 4}f(x)=2$.
Step2: Substitute the value of the limit
Substitute $\lim_{x\rightarrow 4}f(x)=2$ into the expression $3^{\lim_{x\rightarrow 4}f(x)}$. We get $3^{2}$.
Step3: Calculate the result
$3^{2}=9$.
Answer:
9