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A small limit problem

  1. Apr 26, 2009 #1

    alexd

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    1. The problem statement, all variables and given/known data

    lim (x-->infinity) [(sqrt(cosX)-cosX)/(x^2)]

    2. Relevant equations

    hey guys, can anyone please help me solve this limit (without a calculator..)

    10x!
     
    alexd, Apr 26, 2009
  2. jcsd
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  3. Apr 26, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi alexd! Welcome to PF! :smile:

    (have a square-root: √ and an infinity: ∞ :wink:)
    Hint: draw the graph …

    what does it look like? :smile:​

    (erm :redface: … you don't mean limx -> 0, do you?)
     
    tiny-tim, Apr 26, 2009
  4. Apr 26, 2009 #3

    alexd

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    Thanx!

    I drew the graph, it seems to be going to zero when x->∞

    and unfortunetally it is x->∞ and not x->0

    but i'm a bit stuck with the limit...

    any ideas on how to approach it (analytically)?
     
    alexd, Apr 26, 2009
  5. Apr 26, 2009 #4

    tiny-tim

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    ok … so why is it going to 0? …

    how big is the bottom getting? and how big the top? :wink:​
     
    tiny-tim, Apr 26, 2009
  6. Apr 26, 2009 #5

    alexd

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    ok.. I think I see where u're going with this...

    so it's actually not defined when x->∞

    The case for x->0 is much easier - the answer is 1/4...

    is that what u meant?
     
    alexd, Apr 26, 2009
  7. Apr 26, 2009 #6

    tiny-tim

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    Yes :smile:
    Yes it is defined …

    just answer my previous question: how do the top and bottom (separately) behave?
     
    tiny-tim, Apr 26, 2009
  8. Apr 26, 2009 #7

    alexd

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    well...

    the bottom obviously goes to ∞ when x->∞

    and as for the top.. I have no idea...

    that's where i got stuck the 1st time..

    what do you do with cosx when x->∞?

    the graph is attached
     

    Attached Files:

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    alexd, Apr 26, 2009
  9. Apr 27, 2009 #8

    tiny-tim

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    Hi alexd! :smile:

    (i can't see your graph yet, but i assume it's upsy-downsy :wink:)
    Yup! :biggrin:
    I think you're worrying too much about the fact that it obviously doesn't converge :redface:

    but the important point is that it doesn't get out of hand either …

    |cosx| can't be greater than 1 …

    so the top/bottom … ? :smile:
     
    tiny-tim, Apr 27, 2009
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