Explanation Vertical asymptotes of y = x + 1 x Take the denominators of y = x + 1 x and compare to zero x = 0 Check the vertical asymptotes are true lim x → 0 − ( x + 1 x ) lim x → a [ f ( x ) ± g ( x ) ] = lim x → a f ( x ) ± lim x → a g ( x ) = lim x → 0 − ( x ) + lim x → 0 − ( 1 x ) lim x → 0 − ( x ) Plug in the value x = 0 lim x → 0 − ( 1 x ) For x approaching 0 , x < 0 ⇒ x < 0 = − ∞ = 0 − ∞ Apply Infinity Property : c − ∞ = − ∞ = − ∞ lim x → 0 + ( x + 1 x ) lim x → a [ f ( x ) ± g ( x ) ] = lim x → a f ( x ) ± lim x → a g ( x ) = lim x → 0 + ( x ) + lim x → 0 + ( 1 x ) lim x → 0 + ( x ) Plug in the value x = 0 lim x → 0 +

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.5, Problem 58E

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The function of graph the transition points and asymptotes for the equation y = x+1x

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Chapter 4.5, Problem 57E

Chapter 4.5, Problem 59E

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Chapter 4 Solutions

Calculus - Standalone book

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - Prob. 49E Ch. 4.1 - Prob. 50E Ch. 4.1 - Prob. 51E Ch. 4.1 - Prob. 52E Ch. 4.1 - Prob. 53E Ch. 4.1 - Prob. 54E Ch. 4.1 - Prob. 55E Ch. 4.1 - Prob. 56E Ch. 4.1 - 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The function of graph the transition points and asymptotes for the equation y = x + 1 x

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The function of graph the transition points and asymptotes for the equation y = x+1x

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Chapter 4 Solutions