let lim f(x)=4. use the limit rules to find the limit given below. x→3 lim 5^f(x) x→3 lim 5^f(x)=□ x→3…

let lim f(x)=4. use the limit rules to find the limit given below. x→3 lim 5^f(x) x→3 lim 5^f(x)=□ x→3 (simplify your answer.)

let lim f(x)=4. use the limit rules to find the limit given below. x→3 lim 5^f(x) x→3 lim 5^f(x)=□ x→3 (simplify your answer.)

Answer

Explanation:

Step1: Recall limit - exponent rule

If $\lim_{x\rightarrow a}f(x) = L$, then $\lim_{x\rightarrow a}b^{f(x)}=b^{\lim_{x\rightarrow a}f(x)}$, where $b > 0$ and $b\neq1$.

Step2: Substitute the given limit value

Here, $b = 5$, $a = 3$, and $\lim_{x\rightarrow3}f(x)=4$. So, $\lim_{x\rightarrow3}5^{f(x)}=5^{\lim_{x\rightarrow3}f(x)}$. Substituting $\lim_{x\rightarrow3}f(x) = 4$ into the right - hand side, we get $5^{4}$.

Step3: Calculate the result

$5^{4}=5\times5\times5\times5 = 625$.

Answer:

625