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Homework Help: Limit Problem

  1. Nov 23, 2005 #1
    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. jcsd
  3. Nov 23, 2005 #2

    matt grime

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    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
  4. Nov 23, 2005 #3
    This is the right question. Nothing is wrong with it.
  5. Nov 23, 2005 #4
    Is the answer does not exist?
  6. Nov 23, 2005 #5
    do you know L'Hopital's rule that is
    [tex] \lim_{g(x) \rightarrow 0} \frac{f(x)}{g(x)} = \lim_{g(x) \rightarrow 0} \frac{f'(x)}{g'(x)} [/tex]
    if you use that here you should get zero
    also mathematica gives me zero for the answer as well
  7. Nov 23, 2005 #6
    Sorry, I don`t know about L'Hopital's rule.
  8. Nov 23, 2005 #7


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    L'Hopital's rule says that if g and f both have limit 0 as a goes to a, then
    [tex]lim_{x\rightarrow a}\frac{f(x)}{g(x)}= \frac{lim_{x\rightarrow a}f(x)}{lim_{x\rightarrow a}g(x)}[/tex]
    Since, in this problem, the limit of the numerator, [itex]lim_{x\rightarrow 0}x-1[/itex] 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 [itex]-\infty[/itex].
    Some people would say "the limit does not exist". Others would say the limit is [itex]-\infty[/itex] which is just a way of saying the limit does not exist in a particular way.
  9. Nov 23, 2005 #8
    Thanks everyone.
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