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THEOREM 1 (l'Hopital's Rule for zero over zero): Suppose that limx>af(x)=0, limx>ag(x)=0, and that . (Circumvent this indeterminate form by "flipping" vx.)
7 Jun 2010
7 Feb 2009
A second version of L'hopital's rule allows us to replace the limit problem the limit has the indeterminate form 0 / 0 and the first L'hopital's rule can be applied
L'Hospital's Rule Examples for Indeterminate Differences. Recall from the Indeterminate Forms page: Limits in the form \lim_{x\rightarrow a} f(x) - g(x), that is as
So, L'Hospital's Rule tells us that if we have an indeterminate form 0/0 or all we need to do is differentiate the numerator and differentiate the denominator and then take the limit. Before proceeding with examples let me address the spelling of “L'Hospital”. The more modern spelling is “L'Hopital”.
6 Aug 2014
This note provides a number of further examples illustrating L'Hospital's rule. other indeterminate forms the strategy is to modify the given form to turn it into
Other indeterminate forms, such as 1?, 00, ?0, 0. ?, and ? ? ?, can sometimes be evaluated using L'Hopital's rule. For example, to evaluate a limit involving ? ? ?, convert the difference of two functions to a quotient: where L'Hopital's rule is applied when going from (1) to (2) and again when going from (3) to (4).
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