Question

Uniform Convergence

Answer 1

\[\huge{\text{Prove Uniform Convergence }} \]

\[\huge{\text{Let }f_n(x)=\frac{nx}{1+n^2x^2}}\]

Answer 2

\[\text{for } x\ge0\]

Answer 3

\[f_n\left(\frac{1}{n}\right)=\frac{1}{2}\]

Answer 4

I'm just learning about uniform convergence now, and I think I understand how Zarkon got that answer; however, is there an implicit restriction that 1/n has to be greater than zero, or how does that "for x geq 0" restriction work?