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Originally Posted by deltacoder1020
One of the best known applications of this is L'Hopital's rule, which is used for finding the integrals of certain functions that can be transformed into something that resembles one of those patterns - 0/0, inf/inf, inf-inf, 1^inf, 0^0, et cetera.
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L'Hopital's Rule is actually usually used for computing limits. For example, to compute
lim x/sin(x) as x-->0, we can apply L'Hopitals rule to find that
lim x/sin(x) = lim 1/cos x = 1.