Results 1 to 4 of 4

Math Help - [SOLVED] More Limits of Sequences and Series of Functions

  1. #1
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3

    [SOLVED] More Limits of Sequences and Series of Functions

    Please check my work:
    Attached Thumbnails Attached Thumbnails [SOLVED] More Limits of Sequences and Series of Functions-lim2.gif  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    I dont like your proof of (a). I would prefer

    f_n(x) = (1/n) sin(nx),

    so:

    |f_n(x)|<= 1/n

    that is:

    -1/n <= f_n(x) <= 1/n

    and as lim(n->infty) -1/n = lim(n->infty) 1/n =0, we conclude:

    lim(n->infty) f_n(x) =0.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Perhaps I'm missing something here but for (b)

    f_n(x)=(1/n) sin(nx)

    so:

    d/dx f_n(x) = cos(n x)

    Which does not have a limit as n->infty anywhere unless we confine n to N,
    when it will have a limit when x is an integer multiple of pi.

    RonL
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Captain, I would have done things your way under normal circumstances, but i was really tired when i was doing this stuff. the way i messed up the derivative attests to that.

    Thanks for bringing me back to my senses. I'm going home to get some sleep now
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limits of functions and sequences
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 20th 2011, 05:38 PM
  2. sequences and series of functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 30th 2010, 08:33 AM
  3. Replies: 1
    Last Post: November 5th 2009, 09:42 AM
  4. [SOLVED] Series and sequences prob
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 18th 2009, 01:56 AM
  5. [SOLVED] Sequences and series?
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: May 23rd 2009, 04:06 PM

Search Tags


/mathhelpforum @mathhelpforum