1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limit Problem: Itermediate Value Theorem

  1. Nov 15, 2005 #1
    Hello out there. I hope everyone is doing well.
    I could use a little guidance on this:

    suppose [tex]f[/tex] is continuous for all [tex]x[/tex], and

    [tex]\lim_{x\rightarrow -\infty}f(x) = -1[/tex] and [tex]\lim_{x\rightarrow +\infty}f(x) = 10[/tex]

    Show that [tex]f(x) = 0[/tex] for at least one [tex]x[/tex]

    I know I need to use the Intermediate Value Theorem and the definition of the limit...but I'm not really sure how to apply them.

    Thanks,
    Bailey
     
  2. jcsd
  3. Nov 15, 2005 #2

    benorin

    User Avatar
    Homework Helper

    The definition of a limit at infinity will give you some finite value of x for which f(x) is within some neighborhood of 10 (and, seperately, -1). Then use IVT.
     
  4. Nov 15, 2005 #3
    thanks!

    I see it now.

    Bailey
     
  5. Nov 15, 2005 #4

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    try to prove then that every odd degree polynomial has a root.
     
  6. Nov 15, 2005 #5

    benorin

    User Avatar
    Homework Helper

    Nice addition.
     
  7. Nov 15, 2005 #6

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    it was hw problem in frosh calc that i did not get at the time.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Limit Problem: Itermediate Value Theorem
Loading...