Question

as x > infinite what is the limit of ( 1/(a/x) )^ bx

Answer 1

\[\lim_{x\to\infty}\left(\frac{1}{a/x}\right)^{bx}~~?\]

Answer 2

yesss

Answer 3

Depends on \(b\).

Answer 4

it wants the limit usin l'hopitals tho

Answer 5

a should be positive. otherwise you can't compute all powers (i think).

Answer 6

if b > 0 then you basically have infty^infty = infty

Answer 7

if b = 0 you have 1

Answer 8

if b < 0 let c = -b > 0. You have \(\lim_{x\to\infty}\left(\frac{a}{x}\right)^{cx}\). The base alone approaches 0, and an increasing exponent won't stop it.