Pointwise Limit

  • Thread starter sarahp6888
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
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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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