# Is the function uniformly continuous? .

$$f_n (x) = frac {nx} {1 + n ^ 4x ^ 4}$$ , $$x∈ mathbb {R}$$

Fix me $$epsilon> 0$$, searching $$delta> 0$$, so for each $$x, and ∈ mho$$ with $$| x-y | < delta$$ it is valid $$| f (x) -f (y) | < epsilon$$.

So: $$| frac {nx} {1 + n ^ 4x ^ 4} – frac {ny} {1 + n ^ 4y ^ 4} |$$=$$| frac {n (x-y) + n ^ 5xy (y ^ 3-x ^ 3)} {(1 + n ^ 4x ^ 4) (1 + n ^ 4y ^ 4)} |$$

I do not know how I can find a $$delta$$Is there something wrong up?