Explanation Concept used: Use the property of limits to prove f ( x ) = a n x n + a n − 1 x n − 1 + a 1 x + a 0 are the same as the limits of its leading term a n x n as x → ∞ and as x → − ∞ . Take the limit of the function as follows. lim lim → ∞ f ( x ) = lim lim → ∞ ( a n x n + a n − 1 x n − 1 + a 1 x + a 0 ) = lim lim → ∞ ( a n x n ( 1 + a n − 1 a n x n +

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Question

Chapter 1.6, Problem 85P

To determine

To prove: That f(x)=anxn+an−1xn−1+a1x+a0 are the same as the limits of its leading term anxn as x→∞ and as x→−∞ .

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Chapter 1.6, Problem 84A

Chapter 1.6, Problem 86P

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To prove: That f ( x ) = a n x n + a n − 1 x n − 1 + a 1 x + a 0 are the same as the limits of its leading term a n x n as x → ∞ and as x → − ∞ .

Solution Summary: The author uses the property of limits to prove that f(x)=a_nx

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To prove: That f(x)=anxn+an−1xn−1+a1x+a0 are the same as the limits of its leading term anxn as x→∞ and as x→−∞ .

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Chapter 1 Solutions