Question

prove why f(x)=1/x uniformly continuous on (2,infinity )

Answer 1

|f(x)-f(y)|=|1/x-1/y|=|(x-y)/(xy)|<|x-y|/a^2
let delta = a^2*epsilon
then
|f(x)-f(y)|<|x-y|/a^2<epsilon

Answer 2

you could actually get rid of the a variable since x,y are greater than 1.
|x-y|/xy < |x-y|
then choose delta=epsilon and you are good....