Explanation Given information: A function graph is given as, f ( x ) = ( x + 3 x + 2 ) 2 x . Concept used: Horizontal Asymptotes: The line y = L is a horizontal asymptotes of the graph of f if - lim x → ∞ f ( x ) = L or lim x → − ∞ f ( x ) = L L'Hospital's Rule: If f and g are differentiable in an open interval containing a and f ( a ) = g ( a ) = 0 . Also, g ' ( x ) ≠ 0 (except possibly at a ). Then- lim x → a f ( x ) g ( x ) = lim x → a f ' ( x ) g ' ( x ) This rule is also applicable when f ( a ) = ± ∞ and g ( a ) = ± ∞ . Calculation: Given function graph is, f ( x ) = ( x + 3 x + 2 ) 2 x . Suppose, L = lim x → ∞ f ( x ) ⇒ L = lim x → ∞ [ ( x + 3 x + 2 ) 2 x ] ⇒ L = lim x → ∞ e ln [ ( x + 3 x + 2 ) 2 x ] { Since, u = e ln u } ⇒ L = lim x → ∞ e 2 x ⋅ ln ( x + 3 x + 2 ) ⇒ L = e lim

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 4.5, Problem 47PS

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To calculate: The horizontal asymptotes to the graph of the given function.

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Chapter 4.5, Problem 46PS

Chapter 4.5, Problem 48PS

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Chapter 4 Solutions

Calculus

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The horizontal asymptotes to the graph of the given function.

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Chapter 4 Solutions