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Squeeze theorem

  1. Aug 23, 2008 #1
    f(x)=x4 cos(2/x6)

    g(x) <= f(x) <= h(x)

    how to get g(x) and h(x) by using the squeeze theorem??

    I know is something like this -1 <= x <= 1

    But how do i implement it here, and especially to the cos, sin, and tan??
     
  2. jcsd
  3. Aug 23, 2008 #2
    solve the problem!!
     
  4. Aug 23, 2008 #3
    So in your question, [tex]x^4 . cos \frac{2}{x^6}[/tex] what's the limit ie. as x approaches what? zero?

    Then we can use the squeezing theorem; [tex]g(x) \leq f(x) \leq h(x)[/tex]
    Assuming that the limit of f(x) as x approaches c is L then;

    [tex]lim_{x \rightarrow c} g(x) = lim_{x\rightarrowc} h(x) = L[/tex]

    Thus [tex]lim_{x \rightarrow c} f(x) = L[/tex]
     
    Last edited: Aug 23, 2008
  5. Aug 23, 2008 #4

    HallsofIvy

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    What exactly is the question? The "squeeze theorem" refers to limits but you are trying to find the limit of x4cos(2/x6) as x goes to what?


    (And it is your responsibility to "solve the problem"!)
     
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