Does L'Hospital's Rule still apply if the numerator and denominator go to infinity in different directions (i.e. positive infinity over negative infinity)?

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- Jan 24th 2011, 04:17 PMcussetaQuestion Concerning L'Hospital's Rule
Does L'Hospital's Rule still apply if the numerator and denominator go to infinity in different directions (i.e. positive infinity over negative infinity)?

- Jan 24th 2011, 04:27 PMdwsmith
- Jan 24th 2011, 04:44 PMcusseta
For example: The limit as x approaches negative infinity of ( 2x / -e^-x ).

In this example, the numerator approaches**positive**infinity, but the denominator approaches**negative**infinity. - Jan 24th 2011, 04:48 PMdwsmith
- Jan 24th 2011, 04:54 PMHallsofIvy
That is exacly the same as $\displaystyle -\lim_{x\to\infty}\frac{2x}{e^{-x}}$. In general, if one factor goes to "$\displaystyle -\infty$", you can factor out a "-1" and turn the limit into $\displaystyle +\infty$. In other words, it doesn't matter whether the limit is $\displaystyle -\infty$ or $\displaystyle +\infty$.

- Jan 25th 2011, 09:09 AMcusseta
Thanks! I knew it was something ridiculously simple!