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L'Hôpital's Rule
L'Hospital's Rule

A technique used to evaluate limits of fractions that evaluate to the indeterminate expressions and . This is done by finding the limit of the derivatives of the numerator and denominator.

Note: Most limits involving other indeterminate expressions can be manipulated into fraction form so that l'Hôpital's rule can be used.

 

L'Hôpital's Rule:

If f and g are differentiable on an open interval containing a such that g(x) ≠ 0 for all x ≠ a in the interval, and if either

and

or

and

then

Example:

 


  this page updated 21-feb-16
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes