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Pointwise Limit

  1. May 27, 2009 #1
    For the sequence of functions fn(x)=ne^(-xn^2) on [0,infinity), what is the pointwise limit of this sequence?is the converbence uniform?
     
  2. jcsd
  3. May 28, 2009 #2
    Limit functon f(x) is:

    f(x) = 0

    for x > 0

    f(0) is not defined because for x = 0 the sequence diverges.

    Because f(x) is not continuous while all the f_n(x) are continuous, the convergence is not uniform.
     
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