Answer Limit of (x-1)/(x^2)(x+2) as x → 0

[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.

 

[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

 

[frozen7]

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

 

[frozen7]

Is the answer does not exist?

 

[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

 

[frozen7]

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

 

[HallsofIvy]

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.

 

[frozen7]

Thanks everyone.