Answer
$$\lim _{x \rightarrow 4} \frac{x-4}{(x+4)^{0.3}-2} =0$$
Work Step by Step
Given $$\lim _{x \rightarrow 4} \frac{x-4}{(x+4)^{0.3}-2}$$
using the method of replacement
\begin{align*}
\lim _{x \rightarrow 4} \frac{x-4}{(x+4)^{0.3}-2} &=\lim _{x \rightarrow 4} \frac{4-4}{(4+4)^{0.3}-2}\\
&=\lim _{x \rightarrow 4} \frac{0}{(8)^{0.3}-2}\\
&=0
\end{align*}
