Calculating the Limit for sqrt(x^2-9)

[moberry]

Homework Statement

lim sqrt(x^2-9)
x->3

Homework Equations

I understand that the radical will evaluate to 0. I am not sure if the answer to the limit is 0, or undefined

The Attempt at a Solution

lim sqrt((3)^2-9) = sqrt(9-9) sqrt(0) = 0
x->3


Thanks for your help.

 

[Hootenanny]

What is the requirements for a limit to exists?

 

[moberry]

What is the requirements for a limit to exists?

The limit coming from both sides, must approach the same y-value. In this case 0. The function will never hit 0, but will get infinitely close. That would make the value of the limit 0??

 

[Hootenanny]

The limit coming from both sides, must approach the same y-value. In this case 0. The function will never hit 0, but will get infinitely close. That would make the value of the limit 0??

Correct

 

[moberry]

Correct

Good deal. I thought that was it. Wanted to be 100% sure.