# Determining infinite limits

• Sep 2nd 2008, 07:00 PM
NotEinstein
Determining infinite limits
$2x^2(x-1)/(x+1)^3$

limit as x approaches $-1+$ (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 3rd 2008, 12:46 AM
flyingsquirrel
Hello,
Quote:

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

limit as x approaches $-1+$ (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.

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

hence what is the limit of the ratio $\frac{2x^2(x-1)}{(x+1)^3}$ when $x$ tends to $-1^+$ ?
• Sep 3rd 2008, 12:58 AM
Prove It
Quote:

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

limit as x approaches $-1+$ (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, 01:34 AM
mr fantastic
Some editing (in red):

Quote:

Originally Posted by Prove It
The top tends to -4, the bottom tends to $0{\color{red}^{+}}$. 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.