Explanation Given: lim x → c f ( x ) g ( x ) exists but neither lim x → 0 f ( x ) nor lim x → 0 g ( x ) exists. Let the functions f ( x ) = g ( x ) = 1 x , The limits lim x → 0 f ( x ) = , lim x → 0 g ( x ) . The one-sided limit (right side). lim x → 0 + f ( x ) = lim x → 0 + g ( x ) = lim x → 0 + 1 x lim x → 0 + f ( x ) = lim x → 0 + g ( x ) = 1 0 [ apply limit ] lim x → 0 + f ( x ) = lim x → 0 + g ( x ) = + ∞ Increases without bound The one-sided limit (left side) lim x → 0 − f ( x ) = lim x → 0 − g (

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 2, Problem 85SP

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To find the functions f(x) and g(x) such that limx→cf(x)g(x) exists but neither limx→0f(x) nor limx→0g(x) exists.

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Chapter 2, Problem 84SP

Chapter 2, Problem 86SP

Chapter 2 Solutions

Calculus

Ch. 2.1 - Prob. 1PS Ch. 2.1 - Prob. 2PS Ch. 2.1 - Prob. 3PS Ch. 2.1 - Prob. 4PS Ch. 2.1 - Prob. 5PS Ch. 2.1 - Prob. 6PS Ch. 2.1 - Prob. 7PS Ch. 2.1 - Prob. 8PS Ch. 2.1 - Prob. 9PS Ch. 2.1 - Prob. 10PS

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Prob. 41SP Ch. 2 - Prob. 42SP Ch. 2 - Prob. 43SP Ch. 2 - Prob. 44SP Ch. 2 - Prob. 45SP Ch. 2 - Prob. 46SP Ch. 2 - Prob. 47SP Ch. 2 - Prob. 48SP Ch. 2 - Prob. 49SP Ch. 2 - Prob. 50SP Ch. 2 - Prob. 51SP Ch. 2 - Prob. 52SP Ch. 2 - Prob. 53SP Ch. 2 - Prob. 54SP Ch. 2 - Prob. 55SP Ch. 2 - Prob. 56SP Ch. 2 - Prob. 57SP Ch. 2 - Prob. 58SP Ch. 2 - Prob. 59SP Ch. 2 - Prob. 60SP Ch. 2 - Prob. 61SP Ch. 2 - Prob. 62SP Ch. 2 - Prob. 63SP Ch. 2 - Prob. 64SP Ch. 2 - Prob. 65SP Ch. 2 - Prob. 66SP Ch. 2 - Prob. 67SP Ch. 2 - Prob. 68SP Ch. 2 - Prob. 69SP Ch. 2 - Prob. 70SP Ch. 2 - Prob. 71SP Ch. 2 - Prob. 72SP Ch. 2 - Prob. 73SP Ch. 2 - Prob. 74SP Ch. 2 - Prob. 75SP Ch. 2 - Prob. 76SP Ch. 2 - Prob. 77SP Ch. 2 - Prob. 78SP Ch. 2 - Prob. 79SP Ch. 2 - Prob. 80SP Ch. 2 - Prob. 81SP Ch. 2 - Prob. 82SP Ch. 2 - Prob. 83SP Ch. 2 - Prob. 84SP Ch. 2 - Prob. 85SP Ch. 2 - Prob. 86SP Ch. 2 - Prob. 87SP Ch. 2 - Prob. 88SP Ch. 2 - Prob. 89SP Ch. 2 - Prob. 90SP Ch. 2 - Prob. 91SP Ch. 2 - Prob. 92SP Ch. 2 - Prob. 93SP Ch. 2 - 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To find the functions f ( x ) and g ( x ) such that lim x → c f ( x ) g ( x ) exists but neither lim x → 0 f ( x ) nor lim x → 0 g ( x ) exists.

Solution Summary: The author explains how to find the functions f(x) and

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To find the functions f(x) and g(x) such that limx→cf(x)g(x) exists but neither limx→0f(x) nor limx→0g(x) exists.

Want to see the full answer?

Chapter 2 Solutions