1. 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.

2. Hello,
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 $\displaystyle -1^+$ ?

3. 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.

4. Some editing (in red):

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.