Explanation Obtain the value of the function as x approaches 1 . As x approaches 1 , the numerator value becomes, x a − 1 = ( 1 ) a − 1 = 1 − 1 = 0 And the denominator value becomes, x b − 1 = ( 1 ) b − 1 = 1 − 1 = 0 Thus, lim x → 1 x a − 1 x b − 1 = 0 0 is in an indeterminate form. Therefore, apply L’Hospital’s Rule and obtain the limit as shown below

Single Variable Calculus: Early Transcendentals, Volume I

8th Edition

ISBN: 9781305270343

Author: James Stewart

Publisher: Cengage Learning

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0…

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Chapter 4.4, Problem 39E

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To evaluate: The value of limx→1xa−1xb−1 .

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Chapter 4.4, Problem 38E

Chapter 4.4, Problem 40E

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Chapter 4 Solutions

Single Variable Calculus: Early Transcendentals, Volume I

Ch. 4.1 - Explain the difference between an absolute minimum...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Sketch the graph of a function f that is...Ch. 4.1 - Sketch the graph of a function f that is...Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The value of lim x → 1 x a − 1 x b − 1 .

Solution Summary: The author evaluates the value of undersetxto 1mathrmlim

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To evaluate: The value of limx→1xa−1xb−1 .

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Chapter 4 Solutions