How to find whether this function is differentiable

[lax1113]

Homework Statement

F(x)= {1/2x+1 when x=<2
{squareroot(2x) when x=>/=2

is it differentiable at x=2.

Homework Equations

(f(x)-f(2))/(x-2)

The Attempt at a Solution

So i know i ahve to take the limit from both the negative and positive of 2, and determine if they are equal. But after pluggin everyting in i get 0/0 for both equations, and i tried to change the equations a little bit to see if they could reveal the limit, but i coudln't figure it out.

 

[Dick]

You ALWAYS get a 0/0 limit when you apply the definition of derivative. You have to do some algebra to fix that. What form did you get for one of the limits and how did you try to 'fix' it so you get a finite limit?

 

[lax1113]

Hey dick,
Thanks for posting. I went back again a little bit after and it seemed really obvious. I hate how sometimes ill stare at a problem that is very simple and just don't get it, but then i revisit for 2 seconds and it jumps out at me.

I got them to each equal 1/2 after changing them algebraically.