{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Chapter12.3 - Chapter 12.3 Page 527 Definition Asymptotes...

This preview shows pages 1–3. Sign up to view the full content.

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). Page 684 s pital o H L ' ' ^ Rule : If 0 ) ( lim = x f c x and 0 ) ( lim = x g c x , then ) ( ' ) ( ' lim ) ( ) ( lim x g x f x g x f c x c x = . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: 8 6 6 ) ( 2 2 + - - + = x x x x x f , find the hole and the vertical asymptote of f .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern