Question

`lim_(x->oo) ln(x)/x^(1/100)=` ?

Answer 1

`0`

Explanation:

`lim_(x->oo) ln(x)/x^(1/100)=lim_(x->oo)e^(ln(x))/(e^(x^(1/100))) = lim_(x->oo)x/e^(x^(1/100)) = 0`

because `e^(x^alpha)` with `alpha > 0` grows and outperforms any polynomial.