Find . Apply l’Hopital’s rule as many times as necessary, verifying your results after each application

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- Dec 1st 2006, 05:58 PMFLTRl’Hopital’s rule
Find . Apply l’Hopital’s rule as many times as necessary, verifying your results after each application

- Dec 1st 2006, 06:33 PMtopsquark

First both the numerator and denominator go to infinity in the limit, so we can apply L'Hopital's rule.

Thus:

Again, both numerator and denominator go to infinity so:

Again, both numerator and denominator go to infinity so:

Finally, only the numerator goes to infinity and the denominator is a constant, so the net result is:

or more precisely, the limit is undefined.

-Dan - Dec 1st 2006, 06:49 PMTriKri
Just another question, a little of topic maybe, how can one explain so I understand why l’Hopital’s rule is true when ? When it is easier.

- Dec 1st 2006, 06:57 PMtopsquark
- Dec 2nd 2006, 06:21 AMTD!