Question

$\underset{x\to a}{lim}\frac{{(x+2)}^{5/3}-{(a+2)}^{5/3}}{x-a}=$

Answer 1

${lim}_{x\to a}\frac{{(x+2)}^{\frac{5}{3}}-{(a+2)}^{\frac{5}{3}}}{x-a}\left(\frac{0}{0}form\right)$

Using L-Hopital's rule.

${lim}_{x\to a}\frac{5}{3}{(x+2)}^{\frac{2}{3}}\times \left(1\right)\Rightarrow \frac{5}{3}{(a+2)}^{\frac{2}{3}}$