Explanation Given: lim x → ∞ ( 2 x − x + 2 ) Key Concept Applied: The first step to evaluate limits that has square roots in them is to rationalize the expression by multiplying by its conjugate divided by itself. Following this, divide the numerator and the denominator by the largest power in the denominator. The rationalized expression will simplify to f ( x ) = P ( x ) Q ( x ) = a x n + ... b x m + ... , which may resemble one of the three forms given below. The limits are then identified as given. n < m , then lim x → ∞ a x n + ... b x m + ... = 0 n = m , then lim x → ∞ a x n + ... b x m + ... = a b n > m , then lim x → ∞ a x n + ... b x m + ... = + ∞ o r − ∞ based on the sign of a b Case:1 If a b is positive lim x → ∞ a x n + ... b x m + ... = + ∞ Case:2 If a b is negative lim x → ∞ a x n + ... b x m + ... = − ∞ n < m , then lim x → − ∞ a x n + ... b x m + ... = 0 n = m , then lim x → − ∞ a x n + ... b x m + ... = a b n > m , then lim x → − ∞ a x n + ... b x m + ... = + ∞ o r − ∞ based on the sign of a b Case:1 If a b is positive and n − m is odd lim x → ∞ a x n + ... b x m + ... = − ∞ Case:2 If a b is negative and n − m is odd lim x → ∞ a x n + ... b x m + ... = ∞ Case:3 If a b is positive and n − m is even lim x → ∞ a x n + ... b x m + ... = ∞ Case:4 If a b is negative and n − m is even lim x → ∞ a x n + ... b x m + ..

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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Question

Chapter 2.7, Problem 41E

To determine

limx→∞(2x−x+2)

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Chapter 2.7, Problem 40E

Chapter 2.7, Problem 42E

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Chapter 2 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

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