I tutor high school students in Calc and the other day I came across this problem.(adsbygoogle = window.adsbygoogle || []).push({});

Limit of (1-Sqrt(x-2))/(x-3) as x->3

I tried coaching the student on how to simplify the expression and in the end I just showed him this substitution.

Let u=Sqrt(x-2)

Then

(1-Sqrt(x-2))/(x-3) = (1-u)/(u^2-1)

And the Limit becomes

Limit of (1-u)/(u^2-1)=-1/(u+1) as u->1 which is -1/2

He looked at me like I had just done some black magic. I explained substitution to him and why it worked, showed him a couple of other simple examples, and confirmed the answer numerically (like they do in basic calc books when the limit concept is first presented). I still don't think he is 100% convinced because they had not covered this in his class yet which leads to my question.

Can the original problem be solved without substitution?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple Limit Problem

**Physics Forums | Science Articles, Homework Help, Discussion**