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Limit Involving Arctan

  1. Dec 11, 2013 #1
    1. The problem statement, all variables and given/known data

    lim x --> 0 (arctan(cosx))/(e^x)

    a) infinity, b) pi/2, c) pi/4, pi/4 d) -infinity, e) -pi/2

    2. Relevant equations



    3. The attempt at a solution

    You cannot use hospitals rule because its not indeterminate. e^x will approach 1, but I cannot figure out the numerator. Cos(x) will equal 1, but arctan of 1? Any help would be appreciated, exam coming up.

    Thanks!
     
  2. jcsd
  3. Dec 11, 2013 #2

    vela

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    Since ##\tan x = \frac{\sin x}{\cos x}##, you're looking for the angle x such that
    $$\frac{\sin x}{\cos x} = 1 \Rightarrow \sin x = \cos x.$$ This is something you need to know off the top of your head, and if you don't remember it, you look it up.
     
  4. Dec 11, 2013 #3
    oh haha whoops definitely should have thought of that, thanks!
     
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