If f is differentiable at a, where a > 0 and f ' (a) = √ a, then find the value of the following limit. lim x→a ( f(x) − f(a) ) / ( √ x − √ a)

Answer 1

Multiply by [sqrt(x)+sqrt(a)]/[sqrt(x)+sqrt(a)] to get

[f(x)-f(a)]*[sqrt(x)+sqrt(a)]/(x-a)

Then by the Mean Value Theorem the limit becomes sqrt(a)*[sqrt(a)+sqrt(a)]=2a