Question

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

Answer 1

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

$\frac{0}{0}$ apply L'hospital rule

$=\underset{x\to a}{lim}\frac{{\frac{3}{2}(x+2)}^{\frac{1}{2}}-0}{1-0}$

$=\frac{3}{2}\sqrt{a+2}$