Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
10th Edition
ISBN: 9781305657861
Author: Soo T. Tan
Publisher: Cengage Learning
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Chapter B, Problem 1E
To determine

To evaluate: The limit by using l’Hôpital’s Rule.

Expert Solution & Answer
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Answer to Problem 1E

The value of the limit is, limx1x1x21=12 .

Explanation of Solution

l’Hôpital’s Rule:

Suppose f and g are differentiable on an open interval I that contains a, with possible exception of a itself and g(x)0 for all x in I, with possible exception of a. if limxaf(x)g(x) has an indeterminate form of the type 00or  , then limxaf(x)g(x)=limxaf(x)g(x) provided that the limit on the right or is infinite.

Calculation:

Obtain the value of limit limx1x1x21 ,

Since limx1x1x21=00 in an indeterminate form, apply the l’Hôpital’s Rule,

limx1x1x21=limx1ddx(x1)ddx(x21)=limx112x=12(1)=12

Thus, the value of the limit is, limx1x1x21=12 .

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