L’Hôpital’s rule states that given an unresolvable limit of the form or , the ratio of functions will have the same limit at as the ratio . 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 does not prove the nonexistance of .
Example: We try to determine the value of
As 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.
|Date of creation||2013-03-22 12:28:15|
|Last modified on||2013-03-22 12:28:15|
|Last modified by||mathwizard (128)|