Results 1 to 2 of 2

Math Help - Monotonically Increasing

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

    Monotonically Increasing

    For each n \in N let f_{n} : [a,b] \rightarrow R where a,b \in R are such that a < b. Show that if F : [a,b] \rightarrow R is such that F_{n} \rightarrow F as n \rightarrow \infty in a pointwise fashion for each n \in N the function F_{n} is monotonically increasing, then F is monotonically increasing.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Focus's Avatar
    Joined
    Aug 2009
    Posts
    228
    Take x<y, you know that F_n(x)\leq F_n(y). What happens when you tend to the limit as n goes to infinity?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Monotonically Increasing Proof
    Posted in the Differential Geometry Forum
    Replies: 9
    Last Post: January 16th 2011, 06:00 PM
  2. Monotonically increasing
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: November 4th 2010, 05:45 AM
  3. increasing functions prove strictly increasing
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 14th 2010, 04:19 PM
  4. Increasing and Strictly increasing
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 29th 2009, 10:09 AM
  5. Integrating Monotonically Increasing Functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 12th 2009, 08:36 PM

Search Tags


/mathhelpforum @mathhelpforum