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This is a limit an intergral question

  1. Oct 15, 2008 #1
    for n is greater than or equal to 0, let fn (x)= 0, if x is less than n or x is greater than n+1
    1, if x is less than or equal to n+1 and x is greater
    than or equal to n

    a) for each x, find the limit as n approaches infinity of f(x)

    b) for each n, find the integral from -infinity to infinity of fn(x) dx
     
  2. jcsd
  3. Oct 15, 2008 #2

    Mark44

    Staff: Mentor

    What work on this have you done? Do you have any idea what the graph of this function looks like?
     
  4. Oct 16, 2008 #3
    I dont know where to start for the problem and how will i obtain a graph from this problem?
     
  5. Oct 16, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The only way you will obtain the graph is by drawing it yourself! If you are working on integral equations, surely you can graph a function. Here the graph of every fn(x) is just three horizontal straight lines.

    Is it that you are having difficulty reading the definition of the fn?

    Perhaps looking at the first few will help. If n= 0, f0(x) is 0 for x< 0, 1 for x between 0 and 1, and 0 again for x> 1.

    If n= 1, f1[/sup](x) is 0 for x< 1, 1 for x between 1 and 2, and 0 again for x> 2.
    ...
     
    Last edited: Oct 16, 2008
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