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Squeeze Theorem Problem

  1. Jan 1, 2014 #1
    Not sure how to apply the Squeeze Theorem when not given in trig functions.

    My question is.

    Lim (x^2+1)=1
    x→0

    not sure what values lets call them K. ie -K≤x^2+≤K.

    for instances when I have.

    Lim xsin(1/x)=0
    x→0

    i say. -1≤sin(1/x)≤1

    then multiply the whole inequality by x.

    -x≤xsin(1/x)≤x

    therefore limit as x approaches 0 of sin(1/x)=0


    how would I do it for for non trig functions?
     
  2. jcsd
  3. Jan 1, 2014 #2

    tiny-tim

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    Hi TitoSmooth! :smile:

    (try using the X2 button just above the Reply box :wink:)

    You probably wouldn't need it for non-trig (or non-algebraic) functions!

    For example, there's no way of applying it to x2+1.

    wikipedia has an example, involving two variables:

    -|y| ≤ x2y/(x2 + y2) ≤ |y| ​
     
  4. Jan 1, 2014 #3

    vela

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    Yes, there is. There are two very simple functions which bound 1+x2 from above and from below on the interval [-1,1]. The key is that you only need to concern yourself with an interval containing x=0. You don't have to find a simple function that bounds 1+x2 from above for all x.
     
  5. Jan 1, 2014 #4

    Layman terms my man. So I could understand better. Thanks
     
  6. Jan 1, 2014 #5

    HallsofIvy

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    Layman terms? I can see no technical terms in what Vela wrote, except possibly "interval" and vela defined it: "the interval [-1, 1]".
     
  7. Jan 1, 2014 #6
    You don't have to find a simple function that bounds 1+x2 from above for all x.


    missread this. I understand now between the closed interval of -1 and 1
     
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