Results 1 to 2 of 2

Math Help - Pointwise limit

  1. #1
    Member thaopanda's Avatar
    Joined
    Sep 2009
    From
    Worcester, Massachusetts
    Posts
    85

    Pointwise limit

    If possible, find the pointwise limit for the following sequences ({ f_{n}} _{n \in N}:

    a) where for each n \in N the function f_{n}: [-1,1] \rightarrow R is given by f_{n}(x) = \frac{nx}{1 + n^2(x^2)}

    b) where for each n \in N the function f_{n}: R \rightarrow R is given by
    f_{n}(x) =
    1 if x \in [-n,n]
    or 0 if otherwise
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Shanks's Avatar
    Joined
    Nov 2009
    From
    BeiJing
    Posts
    374
    a) f_n tend to 0 for any x in [-1,1]: for if x=0, obviously, it tend to 0; if x=\=0, then nx tend to infinity, and f_n tend to 0.
    b) f_n tend to 1 for any x in R: for any given x in R, there is N such that |x|<N, then if n>N, f_n(x)=1, so it tend to 1 for any x in R.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. pointwise limit.
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: November 10th 2010, 12:13 PM
  2. Pointwise Limit
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: May 16th 2010, 12:23 PM
  3. Pointwise limit
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 23rd 2009, 12:50 AM
  4. Pointwise Limit Please Help!!
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 9th 2009, 08:33 PM
  5. pointwise limit?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 20th 2008, 06:15 PM

Search Tags


/mathhelpforum @mathhelpforum