given lim x→0 f(x)=4 what is the limit? lim x→0 1/4f(x)^4 128 0 4 64

Explanation:

Step1: Apply limit - constant multiple rule

$\lim_{x\rightarrow0}\frac{1}{4}[f(x)]^{4}=\frac{1}{4}\lim_{x\rightarrow0}[f(x)]^{4}$

Step2: Apply limit - power rule

$\frac{1}{4}\lim_{x\rightarrow0}[f(x)]^{4}=\frac{1}{4}(\lim_{x\rightarrow0}f(x))^{4}$

Step3: Substitute the given limit value

Since $\lim_{x\rightarrow0}f(x) = 4$, then $\frac{1}{4}(4)^{4}=\frac{1}{4}\times256 = 64$

Answer:

64