Explanation Given: The limit is lim x → 0 ln ( 1 − x ) x Concept used: Consider f and g are differentiable and g ′ ( x ) ≠ 0 , if lim x → a f ( x ) and lim x → a g ( x ) exist and both are either zero or infinite then the L’ Hôpital’s rule is given as lim x → a f ( x ) g ( x ) = lim x → a f ′ ( x ) g ′ ( x ) The given limit is lim x → 0 ln ( 1 − x ) x Compare the limit lim x → 0 ln ( 1 − x )<

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.5, Problem 3PQ

To determine

To explain:

The reason according to which the given statement “To apply L’ Hôpital’s rule to the limit limx→0ln(1−x)x, the quotient rule is applied to differentiate ln(1−x)x and then the limit is taken” is incorrect.

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Chapter 4.5, Problem 2PQ

Chapter 4.5, Problem 4PQ

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Chapter 4 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

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The reason according to which the given statement “To apply L’ Hôpital’s rule to the limit lim x → 0 ln ( 1 − x ) x , the quotient rule is applied to differentiate ln ( 1 − x ) x and then the limit is taken” is incorrect.

Solution Summary: The author explains that L’ Hôpital’s rule is applied to the limit undersetxto 0mathrmlimmáln(1-

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The reason according to which the given statement “To apply L’ Hôpital’s rule to the limit limx→0ln(1−x)x, the quotient rule is applied to differentiate ln(1−x)x and then the limit is taken” is incorrect.

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Chapter 4 Solutions

The reason according to which the given statement “To apply L’ Hôpital’s rule to the limit lim x → 0 ln ( 1 − x ) x , the quotient rule is applied to differentiate ln ( 1 − x ) x and then the limit is taken” is incorrect.

Solution Summary: The author explains that L’ Hôpital’s rule is applied to the limit undersetxto 0mathrmlimmáln(1-

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To explain: The reason according to which the given statement “To apply L’ Hôpital’s rule to the limit limx→0ln(1−x)x, the quotient rule is applied to differentiate ln(1−x)x and then the limit is taken” is incorrect.

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Chapter 4 Solutions

To explain:

The reason according to which the given statement “To apply L’ Hôpital’s rule to the limit limx→0ln(1−x)x, the quotient rule is applied to differentiate ln(1−x)x and then the limit is taken” is incorrect.