Easy L'Hopitals question

  • Thread starter faust9
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  • #1
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Howdy, I'm stumped by a seemingly easy L'Hopitals limit question.

[tex]\lim_{t\rightarrow 0}\ \frac{\ln t}{t^2-1}[/tex]

I said the limit doesn't exist, but the asker claims it does. I tried various transformations so that I could use L'Hopitals theorm but with no success. I keep getting [tex]\frac{- \infty}{-1}[/tex] so I can't take the derivative of the top and the bottom to get the answer.

Any help would be greatly appreciated.
 

Answers and Replies

  • #2
mathman
Science Advisor
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I think that the problem statement has a minor(?) error, it should be limit for t->1, not 0. Then L'Hospital's can be used (to get 1/2).
 
  • #3
691
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That's what I thought too, but the question was worded as I stated it...

Anyway, thanks for the input.
 
  • #4
HallsofIvy
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Homework Helper
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As stated, L'Hopital's rule does not apply: the numerator goes to infinity and the denominator goes to 1 so the limit does not exist.

The limits as x->1 or as x-> infinity both exist and can be done by L'Hopital. As mathman said, the limit at 1 is 1/2. The limit at
infinity is 0.
 
  • #5
182
0
(-infinity)/(-1) is not an indeterminate form....it equals positive infinity

so the limit can be computed by simply plugging zero and then getting positive infintity
 

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