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Limits involving cosine

  1. Feb 22, 2012 #1
    1. The problem statement, all variables and given/known data
    find the limit of :

    [tex]\lim_{x\rightarrow0}\frac{\sqrt{5-cos(x)}-2}{x^{2}}[/tex]


    2. Relevant equations



    3. The attempt at a solution

    I multiplied the numerator and the denominator by the conjugate of the numerator and i got :

    [tex]\frac{1-cos(x)}{x^{2}(\sqrt{5-cos(x)}+2)}[/tex]

    then: i divided top and bottom by x^2 and i got (1/2)/4 which is 1/8.

    Is what I have done correct?
     
    Last edited: Feb 22, 2012
  2. jcsd
  3. Feb 22, 2012 #2

    tiny-tim

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    hi mtayab1994! :smile:
    oooh, i've never seen that trick before! :tongue2:

    yes, that's fine

    (the usual way of dealing with cosx is to replace it by 1 - x2/2 … same result)
     
  4. Feb 22, 2012 #3
    Yea thanks. And by the way I didn't know that you replace cos x with 1-x^2/2. Well maybe it's because we haven't done it yet.
     
  5. Feb 22, 2012 #4

    tiny-tim

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    ah!

    yes, cos x = 1 - x2/2 + x4/4! - x6/6! + …

    you'll learn about that later :smile:
     
  6. Feb 22, 2012 #5
    Alrighty thank you very much. I live in morocco and i'm in kind of like in a "Math-Science" major in high school so we're really big on math and physics over here.
     
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