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Limits with sinx where x tends to infinity help.

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    I'm having problems in solving the limit which is shown on the gif file .
    As you see I use L'Hopital's rule 2 times and I get to a point when I should divide -sinx with sinx which results in -1 instead of 1 which is the right answer according to the key.

    P.S sorry for posting the same thread in another sub-forum before I came here.
  2. jcsd
  3. Jan 16, 2012 #2


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    You should have stopped after the first differentiation. (1+cos(x))/(1-cos(x)) doesn't have indeterminant form. You can't apply l'Hopital again. And the limit of that expression as x->infinity doesn't exist. So l'Hopital doesn't apply. You'll have to think of another way to find the limit or show one doesn't exist.
  4. Jan 16, 2012 #3
    Solving this limit may help (you can even use l'Hopital's rule!)
    lim x->infinity sinx/x
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