# Finding Limits in a Rational Expression Containing Two Variables

• Sep 28th 2011, 01:00 PM
Pewter12
Finding Limits in a Rational Expression Containing Two Variables
The question I am stuck on is:

lim sp (x+h)² – x²
h→0 spc h

I know that h=0 is undefined because that would make the denominator 0. I also know that if I sub 0 in to solve the limit algebraically, I get 0 as a numerator as well, which I know is indeterminate form.

The problem is, I am not sure how to further factor in order to get h out of the denominator, or if there is even a limit. My textbook says that most often indeterminate form suggests that there is a limit. I am just unsure as to what I should do next.

As for background information, I am new to these topics but generally catch on well enough. I am just looking for a little direction.
• Sep 28th 2011, 01:06 PM
Siron
Re: Finding Limits in a Rational Expression Containing Two Variables
Expand $(x+h)^2=x^2+2xh+h^2$, therefore you get:
$\lim_{h\to 0} \frac{x^2+2xh+h^2-x^2}{h}=\lim_{h\to 0}\frac{2xh+h^2}{h}=\lim_{h\to 0}\frac{h(2x+h)}{h}=...$