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Homework Help: 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

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    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

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

    benorin

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    Nice addition.
     
  7. Nov 15, 2005 #6

    mathwonk

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    it was hw problem in frosh calc that i did not get at the time.
     
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