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Limit of x*cot(x)-1/x^2 as x->0

  1. Jan 26, 2013 #1
    1. The problem statement, all variables and given/known data
    limit x*cot(x)-1/x^2
    x->0



    2. Relevant equations
    lim x*cot(x)=1
    x->0




    3. The attempt at a solution
    it's an indetermination but L'hopital rule doesn't help very much..
     
  2. jcsd
  3. Jan 26, 2013 #2

    Dick

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    Sometimes l'Hopital works better if you try rearranging things. Substitute cot(x)=cos(x)/sin(x). Multiply numerator and denominator by sin(x) and try again.
     
  4. Jan 26, 2013 #3

    haruspex

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    I assume you mean limit (x*cot(x)-1)/x2 as x->0.
    The indeterminacy simply means you've not gone far enough in the expansion of the functions as power series. What expansions do you know for tan x, or failing that, for sin x and cos x?
     
  5. Jan 26, 2013 #4
    thanks Dick, i wish i could see the those simplifications right away!
     
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