Question

point wise convergent fn(x)=x/n​

Answer 1

Answer:

Pointwise convergence of fn(x)=xn

Then if we take the interval 0<x<1, the answer says that this becomes a power sequence which converges to 0. Hence fn(x) ー> f(x) for each fixed x.

Answer 2

Step-by-step explanation:

In that case a pointwise convergent sequence of functions is not uniformly convergent. |fn(x) − f(x)| = xn. ∣ ∣ ∣ ∣fn ( 1 2n )∣ ∣ ∣ ∣ = n, so for no ϵ > 0 does there exist an N ∈ N such that |fn(x) − 0| < ϵ for all x ∈ A and n>N, since this inequality fails for n ≥ ϵ if x = 1/(2n).