14209an3.9-14

14209an3.9-14 - c circlecopyrt Kendra Kilmer February 3 2009 Section 3.3 Infinite Limits and Limits at Infinity Example 1 Let’s examine the

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Unformatted text preview: c circlecopyrt Kendra Kilmer February 3, 2009 Section 3.3 - Infinite Limits and Limits at Infinity Example 1: Let’s examine the behavior of f ( x ) = 1 x 2 − 4 at x = 2. Definition: The vertical line x = a is a vertical asymptote for the graph of y = f ( x ) if 9 c circlecopyrt Kendra Kilmer February 3, 2009 Locating Vertical Asymptotes of Rational Functions If f ( x ) = n ( x ) d ( x ) is a rational function, d ( c ) = 0 and n ( c ) negationslash = 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. Identify all vertical asymptotes. a) f ( x ) = x − 3 x 2 − 4 x + 3 b) g ( x ) = x − 1 ( x + 3 ) 2 c) h ( x ) = 6 x + 9 x 4 + 6 x 3 + 9 x 2 10 c circlecopyrt Kendra Kilmer February 3, 2009 Example 3: Find each limit. Use − ∞ and ∞ when appropriate. a) f ( x ) = x 2 x + 3 i) lim x →− 3 − f ( x ) ii) lim x →− 3 + f ( x ) iii) lim x →− 3 f ( x ) b) g ( x ) = x 2 + x − 2 x + 2 i) lim x →− 2 − g ( x ) ii) lim x →− 2 + g ( x ) iii) lim x →− 2 g ( x ) 11 c...
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This note was uploaded on 03/27/2012 for the course MATH 142 taught by Professor Drost during the Fall '08 term at Texas A&M.

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14209an3.9-14 - c circlecopyrt Kendra Kilmer February 3 2009 Section 3.3 Infinite Limits and Limits at Infinity Example 1 Let’s examine the

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