Let p be a +ve rational number if x^p is defined then lim x--infinity a/x^p = ???

let p be a +ve rational number if x^p is defined then lim x--infinity a/x^p = ???

1 Answer
Jun 26, 2018

lim_(x->oo) a/x^p = 0

Explanation:

Let p=q/d with q,d in NN and mutually prime, then:

x^p = root(d)(x^q)

Now:

lim_(x->oo) x^q = oo

let y=x^q:

lim_(y->oo) root(d)y = +oo

so:

lim_(x->oo) a/x^p = 0