Question

$\underset{x\to a}{lim}\frac{{\left(x+2\right)}^{\frac{5}{2}}-{\left(a+2\right)}^{\frac{5}{2}}}{x-a}$

Answer 1

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

Using $L^{\prime }H$ Rule

$=\underset{x\to a}{lim}\frac{\frac{5}{2}(x+a{)}^{3/2}}{1}$

$=\frac{5}{2}(a+2{)}^{3/2}$