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Squeeze theorem trig question. Please and thanks!

  1. Oct 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Ok, you can see the question and how far I got from the image.

    Lim x--> infinity

    14ieels.jpg

    So, lets take the LEFT side: how does 3x-1 / x turn into just 3?

    I know the answer is 3, but from where you can see in the pic, that is where I get stuck, and dont know how to go on from there.

    THanks!!!

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 13, 2012 #2

    tiny-tim

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    hi nukeman! :smile:
    the 1 becomes insignificant compared to 3x as x -> ∞, so that leaves you with 3x/x, which is 3

    alternatively: (3x-1)/x = 3 - 1/x, and 1/x -> 0 as x -> ∞, so 3 - 1/x -> 3 :wink:
     
  4. Oct 13, 2012 #3
    How does the 1 become insignificant? That is what I am having trouble understanding. :(

    Thanks for the reply :)
     
  5. Oct 13, 2012 #4

    tiny-tim

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    because the 3x becomes 30000 then 30000000000 then 300000000000000 and so on, and the tiddly little 1 doesn't matter much any more :redface:
     
  6. Oct 13, 2012 #5

    SammyS

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    It generally helps us, if you state the problem you're trying to solve.

    In this case it appears to be:
    Find [itex]\displaystyle \lim_{x\,\to\,\infty} \frac{3x+\cos^2(100x)}{x}\ .[/itex]​

    By the way: [itex]0\le \cos^2(100x)\le 1\ .[/itex]
     
  7. Oct 13, 2012 #6
    why is it 0≤ instead of -1?
     
  8. Oct 13, 2012 #7

    SammyS

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    I meant to ask you !
     
  9. Oct 13, 2012 #8
    limit as x -> infinity of [ 3x + cos^{2}(100x)] / x

    I thought it would -1 ≤ cos^2(100x) ≤ 1

    since a cos has amplitude of -1 and 1 ?
     
  10. Oct 14, 2012 #9

    SammyS

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    Right regarding cos(x).

    How about cos2(x)? Is that ever negative?
     
  11. Oct 14, 2012 #10
    wow, how did I NOT know that! :(

    Ok thanks... I got that now.

    So the left side would be 3x/x correct? so, then I would put each term over x, leaving 3 and 1 (3 * 1 = 3) correct?
     
  12. Oct 14, 2012 #11

    SammyS

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    Please write the expression that you're trying to describe .
     
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