- #1
katkat
- 1
- 0
Does anyone know a function t(x) satisfying the following conditions.
as x -> 0 we have
(1) t(x)-> oo
(2) x t(x) -> 0
(3) x t(x) exp(t(x)) -> 0
(4) x t(x)^2 exp(t(x)) -> oo
I have "two extremes" as
t(x) = sqrt(-log x) satisfies (1-3) but x t(x)^2 exp(t(x)) -> 0
t(x) = -log( -x log(x))
satisfies (1-2) and (4), but x t(x) exp(t(x)) -> c >0
I have been searching desperately.
as x -> 0 we have
(1) t(x)-> oo
(2) x t(x) -> 0
(3) x t(x) exp(t(x)) -> 0
(4) x t(x)^2 exp(t(x)) -> oo
I have "two extremes" as
t(x) = sqrt(-log x) satisfies (1-3) but x t(x)^2 exp(t(x)) -> 0
t(x) = -log( -x log(x))
satisfies (1-2) and (4), but x t(x) exp(t(x)) -> c >0
I have been searching desperately.