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

Question

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

1503 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-26T16:47:49

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

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#