Evaluate the following limit: `lim_(x->a)((x+2)^(3//2)-(a+2)^(3//2))/(x-a)`

Explanation

Given limit: `lim_(x->a)((x+2)^(3//2)-(a+2)^(3//2))/(x-a)`
Substituting `a` as we get an indeterminant form of `(0/0)`
As it has come back as `(0/0)` form , so we have a tendency to use L’Hospitals Rule.
now by victimization L’Hospitals Rule the limit is given by,
`l=lim_(x->a)3/2(x+2)^(1/2)`
`=3/2sqrt(a+2)`