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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- January 24th 2011, 05:17 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)?

- January 24th 2011, 05:27 PMdwsmith
- January 24th 2011, 05:44 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. - January 24th 2011, 05:48 PMdwsmith
- January 24th 2011, 05:54 PMHallsofIvy
That is exacly the same as . In general, if one factor goes to " ", you can factor out a "-1" and turn the limit into . In other words, it doesn't matter whether the limit is or .

- January 25th 2011, 10:09 AMcusseta
Thanks! I knew it was something ridiculously simple!