Question

Fn(x)=sqrt((x^2)+(1/n)) and x element of [0,1]
lim Fn(x)=x
∀ε>0, ∀x element of [0,1] ∃Nε,x element of ℕ : ∀n>Nε,x
sqrt((x^2)+(1/n))-x < ε -> ... -> (1/n) / sqrt((x^2)+(1/n))+x < ε and this is where i'm stuck...
How can i find out if it converges uniformly? i'm unable to reduce one side to "n".

Answer 1

\[(1/n)/(\sqrt{x^2+1/n}+x) < \epsilon \]

Answer 2

\[ x \in [0,1] \]

Answer 3

solve to "n"

Answer 4

This is what wolfram alpha come up with, but i don't get it.

Answer 5

that is a big headache