1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.

  2. jcsd
  3. Dec 11, 2013 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted