Explanation Given information : The statement “If lim x → 5 f ( x ) = 0 and lim x → 5 g ( x ) = 0 , then lim x → 5 [ f ( x ) g ( x ) ] does not exist..” Consider the provided statement “If lim x → 5 f ( x ) = 0 and lim x → 5 g ( x ) = 0 , then lim x → 5 [ f ( x ) g ( x ) ] does not exist..” Define f ( x ) = 125 − x 3 and g ( x ) = 5 − x . According to the statement lim x → 5 f ( x ) = 0 and lim x → 5 g ( x ) = 0 . Evaluate the value of lim x → 5 f ( x ) = 0 and lim x → 5 g ( x ) = 0 for defined functions. lim x → 5 f ( x ) = lim x → 5 125 − x 3 = 125 − 5 3 = 125 − 125 = 0 And lim x → 5 g ( x ) = lim x → 5 5 − x = 5 − 5 = 0 Therefore, conditions of the statement are full filled. Recall the quotient law of limits, which is given two functions m ( x ) and n ( x ) the quotient of limit as x tends to k of the individual function is equal to limit of the quotient provided that limit of the denominator is not zero. That is, lim x → k m ( x ) n ( x ) = lim x → k m ( x ) lim x → k n ( x )

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 2, Problem 7TFQ

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To find: Whether the statement “If limx→5f(x)=0 and limx→5g(x)=0 , then limx→5[f(x)g(x)] does not exist.” is true or false.

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Chapter 2, Problem 6TFQ

Chapter 2, Problem 8TFQ

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Chapter 2 Solutions

Biocalculus

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Whether the statement “If lim x → 5 f ( x ) = 0 and lim x → 5 g ( x ) = 0 , then lim x → 5 [ f ( x ) g ( x ) ] does not exist.” is true or false.

Solution Summary: The author explains whether the statement "If undersetxto 5mathrmlimf(x-)=0 and

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To find: Whether the statement “If limx→5f(x)=0 and limx→5g(x)=0 , then limx→5[f(x)g(x)] does not exist.” is true or false.

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Chapter 2 Solutions