Approaching 0: Rationalizing the Limit x→4 √x-4

[heythere1010]

Homework Statement

lim x→4 √x-4
I need to do something so that it is not undefined or 0.

Homework Equations

The Attempt at a Solution

I tried rationalizing, but that just gave me x-4/√x+4, which would still result in an undefined answer.

 

[PeroK]

What exactly is the problem?

 

[heythere1010]

What exactly is the problem?

If I sub in 4 from the beginning, I will get sqrt 0. I can't have that as my answer.

 

[PeroK]

If I sub in 4 from the beginning, I will get sqrt 0. I can't have that as my answer.

Why not?

 

[heythere1010]

Why not?

I thought you would need to do something like conjugates for it.

 

[PeroK]

Not unless you have to prove it from first principles using epsilon-delta.