# Determining infinite limits

• Sep 2nd 2008, 06:00 PM
NotEinstein
Determining infinite limits
$\displaystyle 2x^2(x-1)/(x+1)^3$

limit as x approaches $\displaystyle -1+$ (right hand)

I know the limit approaches negative infinity, but am having a hard time proving my answer by manipulating this function. Thanks in advance.
• Sep 2nd 2008, 11:46 PM
flyingsquirrel
Hello,
Quote:

Originally Posted by NotEinstein
$\displaystyle 2x^2(x-1)/(x+1)^3$

limit as x approaches $\displaystyle -1+$ (right hand)

I know the limit approaches negative infinity, but am having a hard time proving my answer by manipulating this function. Thanks in advance.

$\displaystyle \lim_{x\to-1^+}2x^2(x-1) = ?$ and $\displaystyle \lim_{x\to-1^+}(x+1)^3 = ?$

hence what is the limit of the ratio $\displaystyle \frac{2x^2(x-1)}{(x+1)^3}$ when $\displaystyle x$ tends to $\displaystyle -1^+$ ?
• Sep 2nd 2008, 11:58 PM
Prove It
Quote:

Originally Posted by NotEinstein
$\displaystyle 2x^2(x-1)/(x+1)^3$

limit as x approaches $\displaystyle -1+$ (right hand)

I know the limit approaches negative infinity, but am having a hard time proving my answer by manipulating this function. Thanks in advance.

The top tends to -4, the bottom tends to 0. As a denominator gets very small, the number itself gets very large. So the limit is infinity.
• Sep 3rd 2008, 12:34 AM
mr fantastic
Some editing (in red):

Quote:

Originally Posted by Prove It
The top tends to -4, the bottom tends to $\displaystyle 0{\color{red}^{+}}$. As a denominator gets very small and positive, the number itself gets very large and negative (since the top is negative). So the limit is negative infinity.