# Prove a limit using the mean value theorem

Charlotte87
I am supposed to use the mean-value theorem to show that lim_x→infty(√(x+5)-√(x))=0.

Can anyone help me solving this problem?

I have tried to set up the mean value theorem, but i just do not know how to proceed.

Millennial
It is rather obvious even without the mean value theorem. Just multiply and divide by the conjugate.

Charlotte87
I also believe that the limit is obvious, but the exercise here is to prove it using the mean value theorem.

$$\frac{f(b)- f(a)}{b- a}= f'(c)$$.