Mathematical Analysis for Business II
Mathematical Analysis for Business II MATH 131
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This 2 page Class Notes was uploaded by Theresia Hyatt DDS on Monday September 21, 2015. The Class Notes belongs to MATH 131 at Ohio State University taught by Staff in Fall. Since its upload, it has received 6 views. For similar materials see /class/209942/math-131-ohio-state-university in Mathematics (M) at Ohio State University.
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Date Created: 09/21/15
Section 45 ASYMPTOTES NOTE Polynomial inctions do not have horizontal or vertical asymptotes LI Px 1 and LI Px 7 00 x xaz Vertical Asmptote Rule Let Fm Px Q06 polynomial inctions Where P and Q are The line x a is a vertical asymptote of the gmph of Fx if and only if Qx 0 When Px 0 De nition Ifx a is a vertical asymptote ofthe graph of Fx then at least one of the following conditions must hold LfFXi oo or LfrFXi oo Horizontal Asmptote De nition The line y bis a horizontal asymptote of the gmph of Fx fund only if at least one ofthe following conditions is true Lt Fx b or Lt Fx b x 2 is a vertical asymptote of the gmph of the gmph of Px Similarly x 3 is also a vertical asymptote of the gmph of Px Lt Px0 or Lt Px 0 Hi Hm Therefore y 0 is a horizontal asymptote of the graph of Px Lim H x foo Hiz H Lim Hx o0 H a x 2 is a vertical asymptote ofthe E graph of the graph of H x 7 s 5 LimHx 3 6 Has LimHx 3 Ha mum is a 7 s 5 6 3 2 2 3 6 5 s 7 a a mum Thereforey3isaho zontal asymptote of the gmph of Hx Discuss the vertical and horizontal asymptotes of the graph of the function Gx
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