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"When determining the limit of a quotient f(x)/g(x) when both the numerator and denominator approach 0 or the denominator approaches infinity, <a href="http://en.wikipedia.org/wiki/L%27Hopital%27s_rule"> l'Hôpital's rule</a> states that differentiation of both the numerator and denominator does not change the limit. This differentiation, however, often simplifies the quotient and/or converts it to a determinate form, allowing the limit to be determined more easily."
-From Wikipedia.
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