RedAssign2[1.1 - Then you can apply L’Hôpital’s rule If the top and the bottom are differentiable the limit of the function is equal to the

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Unit: L’Hôpital’s Rule Module: Indeterminate Quotients [page 1 of 1] An Intro to L’Hôpital’s Rule www.thinkwell.com [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. 1540 –rev 08/29/2001 A limit of a function is called an indeterminate form when it produces a mathematically meaningless expression. Indeterminate forms are also called indeterminant forms . L’Hôpital’s rule enables you to evaluate indeterminate forms quickly by using derivatives. For simple functions, their limits can be evaluated easily with simple algebra and direct numerical substitution. For complicated functions it might not be easy to factor or simplify their respective limits, and in some cases algebraic manipulation can be time consuming and lead to errors. Suppose a function has a numerator and a denominator and its limit produces an indeterminate form
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Unformatted text preview: . Then you can apply L’Hôpital’s rule . If the top and the bottom are differentiable, the limit of the function is equal to the limit of the derivative of the numerator divided by the derivative of the denominator. Instead of using algebra, L’Hôpital’s rule enables you to evaluate indeterminate forms quickly by using derivatives. If the quotient of the derivatives still yields an indeterminate form, L’Hôpital’s rule can be applied again. To avoid mistakes, make sure the limit produces an indeterminate form before using L’Hôpital’s rule. CAUTION: Notice that in the example above, the quotient rule is not applied when taking the derivatives. L’Hôpital’s rule doesn’t instruct you to take the derivative of the function. This makes L’Hôpital’s rule easier to use since you do not have to remember the quotient rule....
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This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.

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