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Homework Help: PDEs- pointwise convergence

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data
    fn(x)= e-n*x
    Determine whether or not the sequence fn converges pointwise for each x[tex]\geq[/tex]0

    2. Relevant equations
    when a sequence of functions converges pointwise, the following is satisfied.

    3. The attempt at a solution

    I tried to graph it and I can see that the function shifts down closer and closer to y=0.

    But, I can't really think of a mathematical proof here.

  2. jcsd
  3. Sep 19, 2010 #2
    Dang I thought this was gonna be an actual PDE question. There is really no need to graph nor is there reason for mathematical proof unless you are clueless about the exponential function. Remember for pointwise convergence we only consider what happens by fixing an x in the set under consideration and then letting n approach infinity. Now fix x = 0, what is the limiting function here? Now fix an arbitrary x > 0, what happens when you let n go to infinity then?
  4. Sep 19, 2010 #3

    I'm sorry, my title is misleading. we just went over uniform and pointwise convergence before using it with PDEs :\

    Thank you for the response.

    That was also my logic.

    So, I just say that f(x)= 1 for x=0 and 0 for x>0


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