Results 1 to 3 of 3

Math Help - calc problem

  1. #1
    Newbie
    Joined
    Dec 2006
    Posts
    2

    calc problem

    How do I use calculus to PROVE that the lim as n goes to infinity(n*sin(pi/n)) = n ???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by peprann3213 View Post
    How do I use calculus to PROVE that the lim as n goes to infinity(n*sin(pi/n)) = n ???
    Express it an a Taylor series centered at zero,
    n\left( (\pi/n)-\frac{(\pi/n)^3}{3!}+... \right)
    Distribution laws hold for infinite series,
     \pi -\frac{(\pi/n)^2}{3!}+...
    The limit is clearly zero for all the terms after \pi:
    \pi+0+0+..=\pi
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Another way is the use of a famous limit.
    The convergence of,
    \lim_{x\to \infty} x\sin (\pi/x)
    Is eqivalent tot,
    \lim_{x\to 0} \frac{\sin(\pi x)}{x}
    Thus,
    \lim_{x\to 0} \pi \frac{\sin(\pi x)}{\pi x}
    Thus, (limit composition rule)
    \pi
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. calc problem
    Posted in the Calculus Forum
    Replies: 7
    Last Post: November 27th 2009, 10:08 AM
  2. AP Calc HW problem help (take 2)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 18th 2009, 04:00 PM
  3. Calc Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 31st 2008, 07:27 PM
  4. Help with Calc problem....
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 15th 2008, 02:36 PM
  5. Calc II problem
    Posted in the Calculus Forum
    Replies: 8
    Last Post: May 18th 2007, 08:24 AM

Search Tags


/mathhelpforum @mathhelpforum