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

Question

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

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Answer 1 · 2017-08-16T13:22:36

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

#(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#