Limit Problem

1. Nov 23, 2005

frozen7

lim (x-1) / (x^2)(x+2) as x approach to 0

Is the answer equal to zero??

No matter what mathod I use ,the answer I got are all the same.

2. Nov 23, 2005

matt grime

the numerator tends to -1 the denominator to zero, doesn't that tell you something? It seems quite simple so perhaps you copied the question down wrongly

3. Nov 23, 2005

frozen7

This is the right question. Nothing is wrong with it.

4. Nov 23, 2005

frozen7

Is the answer does not exist?

5. Nov 23, 2005

stunner5000pt

do you know L'Hopital's rule that is
$$\lim_{g(x) \rightarrow 0} \frac{f(x)}{g(x)} = \lim_{g(x) \rightarrow 0} \frac{f'(x)}{g'(x)}$$
if you use that here you should get zero
also mathematica gives me zero for the answer as well

6. Nov 23, 2005

frozen7

Sorry, I don`t know about L'Hopital's rule.

7. Nov 23, 2005

HallsofIvy

Staff Emeritus
L'Hopital's rule says that if g and f both have limit 0 as a goes to a, then
$$lim_{x\rightarrow a}\frac{f(x)}{g(x)}= \frac{lim_{x\rightarrow a}f(x)}{lim_{x\rightarrow a}g(x)}$$
Since, in this problem, the limit of the numerator, $lim_{x\rightarrow 0}x-1$ is -1, not 0, LHopital's rule does not apply.
As x approaches 0, the numerator stays around -1 while the denominator goes to 0: the fraction goes toward $-\infty$.
Some people would say "the limit does not exist". Others would say the limit is $-\infty$ which is just a way of saying the limit does not exist in a particular way.

8. Nov 23, 2005

frozen7

Thanks everyone.