# Limit of square root function

Could someone help me with this? I feel it should likely be easy, but I'm baffled anyway:

## Homework Statement

Prove the validity of the limit lim x -> x_0 sqrt(x) = sqrt(x_0)

## Homework Equations

use definition of limit

## The Attempt at a Solution

Mark44
Mentor
You want to show that for any delta > 0, there is an epsilon so that |sqrt(x) - sqrt(x_0)| < eps when |x - x_0| < delta.

|sqrt(x) - sqrt(x_0)| = |sqrt(x) - sqrt(x_0)| *|sqrt(x) + sqrt(x_0)| /|sqrt(x) + sqrt(x_0)| = |x - x_0|/ *|sqrt(x) + sqrt(x_0)|

Without loss of generality, you can assume that delta is reasonably small, say less than 1. That puts x within 1 unit of x_0.

Can you work with |sqrt(x) + sqrt(x_0)| to find max and min values for it?

Okay...this is starting to make more sense now. Thanks for the tips. When I get it I'll try to upload what I have.