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Slavakion, to give you an example of when L'Hôpital's rule is applied, take <sup>(2<sup>x</sup> - 1)</sup>/<sub>x</sub> when x is zero. That is a zero over zero case, but they are not necessarily the "same" zero, as it was explained to me in geometry. Graph that and look what happens when x is near zero, but evaluate it at zero.
Another example of when dealing with zeros, have <sup>(2<sup>x</sup> - 8)</sup>/<sub>(x - 3)</sub>. Evaluate it at 3, no answer, but it looks like there should be an answer as you get closer to it. You'll find that it should be approaching 8*Ln(2).
[And yes, I was that kid you threw pencils at when my hand went up with a question everyone knew had nothing to do with geometry, and more of that math the teacher called "calculus."]
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