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

Question

2376 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-04T19:09:59

$0$

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

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

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