# Small Limit Problem

• Jun 5th 2009, 08:29 PM
Kasper
Small Limit Problem
Hey, so I have this limit question, and I'm *pretty* sure that the limit does not exist, but I get my back up, because anyone could come to an answer like that from not knowing a way to simplify it. Can anyone see a way to simplify this and get a value?

Thanks for any help!

$\displaystyle lim_{x->1}\frac{x^3+x^2}{x-1}$

Also, sorry for the dumb looking "approaches" arrow in the limit, I couldn't find the code for a good arrow in the LaTeX tutorial. :(
• Jun 5th 2009, 09:18 PM
mr fantastic
Quote:

Originally Posted by Kasper
Hey, so I have this limit question, and I'm *pretty* sure that the limit does not exist, but I get my back up, because anyone could come to an answer like that from not knowing a way to simplify it. Can anyone see a way to simplify this and get a value?

Thanks for any help!

$\displaystyle lim_{x->1}\frac{x^3+x^2}{x-1}$

Also, sorry for the dumb looking "approaches" arrow in the limit, I couldn't find the code for a good arrow in the LaTeX tutorial. :(

$\displaystyle lim_{x \rightarrow 1^+} \frac{x^3+x^2}{x-1} = + \infty$

$\displaystyle lim_{x \rightarrow 1^-} \frac{x^3+x^2}{x-1} = - \infty$

Since the left hand and right hand limits are not equal, the limit does not exist.
• Jun 5th 2009, 10:50 PM
Kasper
Ah right, I was looking at it all wrong. I keep trying to just simplify f(x) to find a way to sub in x and try to algebraically find an answer, I gotta start working on thinking of how the limit approaches rather than trying to find it when it's at the point in question.

Thanks for the clarification!