# Evaluate the Limit of:

1. Oct 20, 2011

### Jimbo57

1. The problem statement, all variables and given/known data
[PLAIN]http://www4b.wolframalpha.com/Calculate/MSP/MSP32119hfegi8c73g07i600000h48cbcha52cc1ce?MSPStoreType=image/gif&s=5&w=78&h=46 [Broken]
As x approaches 2.

2. Relevant equations

3. The attempt at a solution
I rationalize the denominator and that doesn't work as it gives me another undefined answer. I just finished learning the Squeeze Theorem, so I'm guessing that I may have to use that, although I don't have a clue on how to apply it here. That or the limit simply doesn't exist. Am I way off? Where would the pros start with this one?

Last edited by a moderator: May 5, 2017
2. Oct 21, 2011

### dynamicsolo

Ah, I remember this one: is this out of Stewart's book? (If not, it's probably originally from the Russian collection "everyone" steals from...)

Did you try using a "conjugate factor" on the denominator, when you say you tried "rationalizing" it? Doesn't quite do the job, but it's a start. The "trick" is to also use a conjugate factor for the numerator: you want to get rid of the troublesome differences that go to zero. If you use the two conjugate factors, you'll find the troubles all clear up.

And I can tell you that the Squeeze Theorem is of no help here...

3. Oct 21, 2011

### Staff: Mentor

What dynamicsolo said works. The trick is rationalizing both numerator and denominator.

4. Oct 21, 2011

### NewtonianAlch

So do you mean to multiply the fraction by the conjugate of the denominator for both the numeratory and denominator, or is it to multiply the fraction by the conjugate of the numerator over the denominator?

5. Oct 21, 2011

### SammyS

Staff Emeritus
Neither.

multiply the fraction by the conjugate of the denominator for both the numerator and denominator

AND

multiply the fraction by the conjugate of the numerator for both the numerator and denominator

6. Oct 21, 2011

### Jimbo57

It is from Stewart! Hah, good call. Thanks for the tip Dynamicsolo, I'll give it a go for sure.