13112an2.13-18

# 13112an2.13-18 - c Kendra Kilmer Section 2.5 Limits...

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c c Kendra Kilmer January 11, 2012 Section 2.5 - Limits Involving Infinity Example 1: Let’s examine the behavior of f ( x ) = 7 x x 2 at x = 0. Definition: The vertical line x = a is a vertical asymptote for the graph of y = f ( x ) if 13

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c c Kendra Kilmer January 11, 2012 Locating Vertical Asymptotes of Rational Functions If f ( x ) = n ( x ) d ( x ) is a rational function, d ( c ) = 0 and n ( c ) n = 0, then the line x = c is a vertical asymptote of the graph of f . Example 2: Describe the behavior of f at each discontinuity. f ( x ) = x 3 x 2 4 x + 3 Example 3: Find each limit. Use and when appropriate. a) lim x →− 3 x 2 x + 3 b) lim x →− 2 x 2 + x 2 x + 2 14
c c Kendra Kilmer January 11, 2012 Limits at Infinity Example 4: Let’s examine the behavior of x 2 and 1 x 2 as x approaches positive and negative infinity. Limits of Power Functions at Infinity If p is a positive real number and k is any real constant, then 1. lim x kx p 2. lim

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## This note was uploaded on 04/01/2012 for the course MATH 131 taught by Professor Allen during the Fall '08 term at Texas A&M.

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13112an2.13-18 - c Kendra Kilmer Section 2.5 Limits...

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