Question

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

Answer 1

lim $\frac{(x+2)3/2-(a+2)3/2}{x-a}$ -----(1)

$x\to a$

$\Rightarrow$ on differtating eq(1)using L Hosptal rule

$\Rightarrow lim$ $\frac{\frac{3}{2}(x+2)1/2-0}{1}$ =lim $\frac{3}{2}$(x+2)1/2$

$x\Rightarrow a$ $x\Rightarrow a$

$\Rightarrow$ appling limit

$\Rightarrow \frac{3}{2}(a+2)1/2$