What is the Limit of that ? lim_(xrarroo) (2/3)^x

Lim (2/3)^x
x--> infinity

1 Answer
Aug 16, 2017

lim_(xrarroo) (2/3)^x = 0

Explanation:

(2/3)^x = e^(xln(2/3))

ln(2/3) < 0 so

as xrarroo,

xln(2/3)rarr-oo

So " " e^(xln(2/3)) rarr 0 as xrarroo.

General rule

For 0 < a < 1, we have lim_(xrarroo)a^x = 1