Explanation Given: The limit function is lim x → 1 ( x 2 − 5 x + 4 x 3 − 1 ) . Formula used: The identity is: a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 ) Calculation: The limit function is lim x → 1 ( x 2 − 5 x + 4 x 3 − 1 ) . Now, find the limit. First, transform algebraically the function. Factorize the numerator by splitting the terms. x 2 − 5 x + 4 = x 2 − 4 x + x + 4 Factorize the terms. x 2 − 5 x + 4 = x 2 − 4 x − x + 4 = x ( x − 4 ) − 1 ( x − 4 ) = ( x − 4 ) ( x − 1 ) Use the identity in the denominator. x 3 − 1 = x 3 − 1 3 = ( x − 1 ) ( x 2 + x + 1 ) Substitute the factors in the function

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 2.5, Problem 39E

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Evaluate the function by using the identity a3−b3=(a−b)(a2+ab+b2).

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Chapter 2.5, Problem 38E

Chapter 2.5, Problem 40E

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Evaluate using the identity a3 - b3 = (a-b)(a2+ab+b2)

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Chapter 2 Solutions

Calculus - Standalone book

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 5PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E

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Evaluate the function by using the identity a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 ) .

Solution Summary: The author explains how to determine the value of the limit function by using the identity a3-b3.

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Evaluate the function by using the identity a3−b3=(a−b)(a2+ab+b2).

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Chapter 2 Solutions