Question

what is L' hospital rule

Answer 1

In calculus, l'Hôpital's rule pronounced: [lopiˈtal] (also sometimes spelled l'Hospital's rule with silent "s" and identical pronunciation), also called Bernoulli's rule, uses derivatives to help evaluate limits involving indeterminate forms. Application (or repeated application) of the rule often converts an indeterminate form to a determinate form, allowing easy evaluation of the limit. The rule is named after the 17th-century French mathematician Guillaume de l'Hôpital, who published the rule in his book Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes (literal translation: Analysis of the Infinitely Small for the Understanding of Curved Lines) (1696), the first textbook on differential calculus.[1][2] However, it is believed that the rule was discovered by the Swiss mathematician Johann Bernoulli.[3]
The Stolz-Cesàro theorem is a similar result involving limits of sequences, but it uses finite difference operators rather than derivatives.

Answer 2

http://mathworld.wolfram.com/LHospitalsRule.html

Answer 3

http://tutorial.math.lamar.edu/Classes/CalcI/LHospitalsRule.aspx

Answer 4

http://www.math.psu.edu/dlittle/java/calculus/lhospital.html

Answer 5

Suppose you are taking a limit in the form:
\[\lim_{x\rightarrow a}\frac{f(x)}{g(x)}\]Then if \(f(a)/g(a)\) is an indeterminate form, then the following is true:\[\lim_{x\rightarrow a}\frac{f(x)}{g(x)}=\lim_{x\rightarrow a}\frac{f^\prime (x)}{g^\prime (x)}\]

Answer 6

AT LAST AND BEST http://www.khanacademy.org/math/calculus/differential-calculus/v/introduction-to-l-hopital-s-rule