Results 1 to 3 of 3

Math Help - Prove that there exists a positive integer n

  1. #1
    Member
    Joined
    Oct 2009
    From
    Canada
    Posts
    128

    Prove that there exists a positive integer n

    1. Suppose delta > 0.


    (a) Prove that there exists a positive integer n such that

    0 < 1/((4n+1)pi/2) < delta

    and sin ((4n+1)pi/2) = 1


    (b) Prove that there exists a positive integer m such that

    0 < 1/((4m+3)pi/2) < delta

    and sin ((4m+3)pi/2) = -1



    see if anyone can do it,
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    Quote Originally Posted by 450081592 View Post
    1. Suppose delta > 0.


    (a) Prove that there exists a positive integer n such that

    0 < 1/((4n+1)pi/2) < delta

    and sin ((4n+1)pi/2) = 1


    (b) Prove that there exists a positive integer m such that

    0 < 1/((4m+3)pi/2) < delta

    and sin ((4m+3)pi/2) = -1



    see if anyone can do it,
    For the first one take n> \frac{1}{4} (\frac{1}{ \delta \pi /2} -1 ) (just isolate n) and note that \sin ((4n+1) \pi /2)=\sin (2n\pi ) \cos (\pi /2) + \sin (\pi /2) \cos (2n \pi )=\sin (\pi /2)=1. For the second one do exactly the same thing, the only difference being \sin (3\pi /2)=-1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    From
    Canada
    Posts
    128

    what does this imply? I cant see the connection between this and n to be an positive integer, can you explain it please
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: December 8th 2011, 08:16 AM
  2. Replies: 9
    Last Post: April 6th 2010, 11:12 PM
  3. Replies: 2
    Last Post: February 22nd 2009, 02:49 PM
  4. Replies: 2
    Last Post: February 5th 2009, 02:27 PM
  5. Replies: 2
    Last Post: October 14th 2007, 05:32 AM

Search Tags


/mathhelpforum @mathhelpforum