Pointwise limit and uniform convergence of fn(x)=ne^(-xn²)

[sarahp6888]

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?

 

[Count Iblis]

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.