l’Hôpital’s rule

L’Hôpital’s rule states that given an unresolvable limit of the form 00 or , the ratio of functions f(x)g(x) will have the same limit at c as the ratio f(x)g(x). In short, if the limit of a ratio of functions approaches an indeterminate form, then


provided this last limit exists. L’Hôpital’s rule may be applied indefinitely as long as the conditions are satisfied. However it is important to note, that the nonexistance of limf(x)g(x) does not prove the nonexistance of limf(x)g(x).

Example: We try to determine the value of


As x approaches the expression becomes an indeterminate form . By applying L’Hôpital’s rule twice we get


Another example of the usage of L’Hôpital’s rule can be found http://planetmath.org/node/5741here.

Title l’Hôpital’s rule
Canonical name LHopitalsRule
Date of creation 2013-03-22 12:28:15
Last modified on 2013-03-22 12:28:15
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 13
Author mathwizard (128)
Entry type Theorem
Classification msc 26A24
Classification msc 26C15
Synonym l’Hospital’s rule
Related topic IndeterminateForm
Related topic DerivationOfHarmonicMeanAsTheLimitOfThePowerMean
Related topic ImproperLimits
Related topic ExampleUsingStolzCesaroTheorem