Question

How do you find the limit of `((e^x)-x)^(2/x)` as x approaches infinity?

Answer 1

`e^2`

Explanation:

`(e^x-x)^(2/x) = (e^x(1-x/e^x))^{2/x} = e^2(1-x/e^x)^{2/x}`

but

`lim_{x->oo}(1-x/e^x)^{2/x}=1` so

`lim_{x->oo}(e^x-x)^(2/x)=e^2`