Evaluate Limit in Terms of Derivative

[lawrencese]

If f is differentiable at x=a where a>0, evaluate the following limit in terms of f'(a):

lim as x tend to a

f(x) - f(a)
----------------
sqrt(x) - sqrt (a)

I don't really understand what it means to evaluate in terms of the derivative...

 

[tkhunny]

It's not clear to me what is wanted, but I did have one idea that might lead to something.

If x = a+h, change the limit to h approaching zero.

Rewrite: \(\displaystyle \frac{f(a+h)-f(a)}{\sqrt{a+h}-\sqrt{a}}=\frac{\frac{f(a+h)-f(a)}{h}}{\frac{\sqrt{a+h}-\sqrt{a}}{h}}\)