Chapter12.3 - Chapter 12.3 Page 527. Definition:...

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Chapter 12.3 Asymptotes, Hole and L’Hopital’s Rule. Page 527. Definition: Given a rational function, ) ( ) ( ) ( x q x p x f = . The domain is the set of all real numbers except the solution(s) to 0 ) ( = x q . (i) If f ( x ) has a limit at a solution to 0 ) ( = x q , then f has a hole at that point; (ii) If f ( x ) does not have a limit at a solution to 0 ) ( = x q , then the solution is a vertical asymptote . Example 1: 1 2 ) ( 2 2 - - + = x x x x f , find the hole and the vertical asymptote of f . 1 st . Solve ( 29 ( 29 1 , 1 0 1 1 0 1 2 = - = = - + = - x x x x x q q 2 nd . Evaluate ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 real x x x x x x x f undefined x x x x x x x f x x x x x x = + + = - + + - = = = + + = - + + - = - - - 2 3 1 2 lim 1 1 2 1 lim ) ( lim ! 0 1 1 2 lim 1 1 2 1 lim ) ( lim 1 1 1 1 1 1 So, f has a vertical asymptote, x = – 1; f has a hole at x = 1 and the location of the hole is 2 3 , 1 . (See Figure 2).
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This note was uploaded on 04/09/2008 for the course MAT 220 taught by Professor For during the Spring '08 term at Community College of Allegheny County.

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Chapter12.3 - Chapter 12.3 Page 527. Definition:...

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