3.6.notes.a

# 3.6.notes.a - f x =-∞ but it is not needed now because we...

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MAC 2233/001-006 Business Calculus, Fall 2011 CRN: 81700–81702, 81705, 81716, 81715 Assistants : Matthew Fleeman, Arbin Rai, Tadesse Zerihun, Vindya Kumari, Junyi Tu, Jing- han Meng An example on fnding vertical and horizontal asymptotes Example . Find all vertical and horizontal asymptotes: f ( x ) = x 2 +4 x - 2 . Solution. For vertical asymptotes, we fnd that the only candidate is x - 2 = 0 , that is , x = 2 . To check i± x = 2 is in ±act an asymptote, we fnd that lim x 2 + f ( x ) = lim x 2 + x 2 + 4 x - 2 = , and so x = 2 is indeed a vertical asymptote. (One can check that lim x 2 -
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Unformatted text preview: f ( x ) =-∞ , but it is not needed now because we already know lim x → 2 + f ( x ) = ∞ .) For horizontal asymptotes, we fnd that as x → ∞ , f ( x ) ≈ √ x 2 x = | x | x = x x = 1 . That is, lim x →∞ f ( x ) = 1 , and y = 1 is a horizontal asymptote . Also, as x → -∞ , f ( x ) ≈ √ x 2 x = | x | x =-x x =-1 . That is, lim x →-∞ f ( x ) =-1 , and y =-1 is a horizontal asymptote . The graph o± the ±unction is given below: x K 6 K 4 K 2 2 4 6 y K 6 K 4 K 2 2 4 6...
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