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 with tangent

  1. Jan 25, 2008 #1
    1. The problem statement, all variables and given/known data

    Solve the following limit:

    [tex]\lim_{x \rightarrow 1}(1-x)\tan{\left(\frac{\pi x}{2}\right)}[/tex]

    3. The attempt at a solution

    I solved it using L'Hospital rule, it's equal to 2/pi, but is there any other way how to solve it? thanks a lot!

    The same question would apply to

    [tex]\lim_{x \rightarrow \frac{\pi}{3}}\left(\frac{\sin{\left(x-\frac{\pi}{3}\right)}}{1-2\cos{x}}\right)[/tex]
    Last edited: Jan 25, 2008
  2. jcsd
  3. Jan 27, 2008 #2
    Well, I've finally found a different way how to solve it... I post it here since it can be useful to someone..

    I substituted x with y = x-1, and then after some steps I've arrived at the following limit:

    [tex]\lim_{y \rightarrow 0}\frac{\frac{\pi}{2}y}{\sin{\frac{\pi}{2}y}}\frac{2}{\pi}\cos{\frac{\pi}{2}y} = \frac{2}{\pi}[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook