Question

b) Show, that the sequence of functions \(f(x)=\frac{x}{n}\) converges point wise but not uniformly on \(\mathbb{R}\).

Answer 1

It Does not converge pointwise.

It converge pointwise but the limit is not continous.

It converge pointwise but not uniformly.

It converge uniformly.

Answer 2

its some points

Answer 3

Can you show that mathematically ?

Answer 4

well, limit function is 0 clearly, clearly sup\[\huge\ |f_n(x)−0|→0 \]as \[\huge\ n→∞\] and \[\huge\ x∈[0,1] \]so, it converges uniformly to 0 am I right? so in my guess, 4 is only correct.

Answer 5

@tunahan

Answer 6

ok thank you Ron.mystery