Section4-5 - Section 4.5 Indeterminate Forms and...

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1 Section 4.5 Indeterminate Forms and l’Hospital’s Rule • Goals – Introduce the various types of indeterminate forms – Find limits of indeterminate forms using l’Hospital’s Rule . Introduction Suppose we want to analyze the behavior of the function • Since… – the limit of the denominator as x 1 is 0 , we cannot use Limit Laws to find – the limit of the numerator is also 0 as x 1 , it is not even clear whether the limit exists at all. ( ) = = ln near 1. 1 x F x x x ( ) 1 lim ; x F x L’Hospital’s Rule Here is a way to evaluate such limits: L’Hospital’s Rule (cont’d) Some remarks: – L’Hospital’s Rule says that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives . – Be sure to verify the required conditions on f and g before using l’Hospital’s Rule. – L’Hospital’s Rule is also valid for one-sided limits and for limits at or – .
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