Find δ(a; ε) for the given f and J.

f(x) = lnx, J = (0,∞)

I have let ε > 0 and δ = ? s.t. if x, y belong to J and |x-y| <δ then |f(x)-f(y) | < ε

so | f(x)-f(y) | = | ln(x) - ln(y) | we want this less that epsilon. From here I'm not sure I can do this but i did.

e^| ln(x) - ln(y) | = | x - y | < e^(ε). ----------------- Not sure if I can do this step!

So we want δ = e^(ε).

Then I just restate this formely:

et ε > 0 and δ = e^(ε). s.t. if x, y belong to J and |x-y| <δ then |f(x)-f(y) | < ε

Does this seem right?