NOTES 1.5 Continuity on Intervals & IVT.pdf - Notes 1.5 Continuity Continued IVT §1.5—Continuity Continued IVT A continuous function A

NOTES 1.5 Continuity on Intervals & IVT.pdf - Notes 1.5...

This preview shows page 1 - 4 out of 8 pages.

Notes 1.5: Continuity Continued & IVT Page 1 of 8 §1.5—Continuity Continued & IVT A continuous function A non-continuous function To review the 3-step definition of continuity at a point, A function ( ) f x is continuous at a point x c = if ( ( ( lim lim x c x c f x f c f x - + = = Example 1: Determine the values at which the function ( 29 2 1 , 2 3 2 5, 2 2 , 2 4 8 , 4 x x x x f x x x x x < - + - < = < is continuous, then find ( lim x f x →-∞ and ( lim x f x →∞ .
Image of page 1
Notes 1.5: Continuity Continued & IVT Page 2 of 8 Continuity on an interval A function ( f x is continuous on an interval I , if and only if the function ( f x is continuous at every point in the interval I . More specifically, Continuity on an open interval A function ( f x is continuous on an open interval ( , a b if and only if the function ( f x is continuous at every point in the interval ( , a b . Additionally, Continuity on a closed interval A function ( ) f x is continuous on a closed interval [ ] , a b if it is continuous on the open interval ( , a b and if the endpoints exhibit the following: (i) lim ( ) ( ) x a f x f a + = and (ii) lim ( ) ( ) x b f x f b - = Example 2: The graph of ( f x is given below. Determine the largest intervals 0 x 3 for which the function f x ( is continuous.
Image of page 2
Notes 1.5: Continuity Continued & IVT Page 3 of 8 Example 3: The graph of a familiar function ( f x is given below. Answer the following questions based on the graph of ( f x .
Image of page 3
Image of page 4

You've reached the end of your free preview.

Want to read all 8 pages?

  • Fall '14
  • Reinke

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors