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

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Chapter 2 Solutions

Calculus

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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.

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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 Solutions