calc notes lecture 18

calc notes lecture 18 - 1 1 lim 0 0 and lim 0 0 r r x x r r...

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Lecture Section Objectives Assignment 18 3.6 Asymptotes 3.6: 1-35 eoo, 39, 41, 53, 61, 63 Understanding Goals: 1. Understand how vertical asymptotes of functions are defined and know how to find them and find infinite limits. 2. Understand how horizontal asymptotes of functions are defined and know how to find them and find limits at infinity. 3. Understand how to use asymptotes to answer real-life situations. Example 1 : Find each limit. a) 1 1 lim 1 x x - - 1 1 lim 1 x x + - b) 1 1 lim 1 x x - - - 1 1 lim 1 x x + - - c) 2 1 1 lim ( 1) x x - - - 2 1 1 lim ( 1) x x + - - d) 2 1 1 lim ( 1) x x - - 2 1 1 lim ( 1) x x + - 1
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Example 2 : Find the vertical asymptotes of the graph of a) 2 1 ( ) x f x x x + = - b) 2 2 4 5 ( ) 1 x x f x x + - = - 2
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Recall that
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Unformatted text preview: 1 1 lim 0, 0 and lim 0, 0 r r x x r r x x-= = Example 3 : Find the limit a) 2 1 lim 2 x x f-b) 3 1 lim 5 x x y-+ 3 Example 4 : Find the horizontal asymptote of the graph of each function: a) 2 5 7 4 3 x y x-+ = + b) 2 2 5 7 4 3 x y x-+ = + c) 3 2 5 7 4 3 x y x-+ = + 4 Example 5 : Find vertical and horizontal asymptotes of following functions: a) ( 29 2 2 5 6 9 x x g x x + + =-b) ( 29 6 3 9 1 x x f x x-= + 5 Example 6 : Sketch the graph of the equation 3 2 x y x-=-. Use intercepts, extrema, and asymptotes as sketching aids. 6...
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This note was uploaded on 04/17/2008 for the course MAT 111 taught by Professor Fan during the Spring '08 term at Union.

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calc notes lecture 18 - 1 1 lim 0 0 and lim 0 0 r r x x r r...

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