Question

Find the limit if it exists:

lim x->infinity

[1+(1/2x)]^3x

Answer 1

as x goes towards infinity the 1/2x part of the term becomes insignificant since it is practically 0

Answer 2

that means the term can be reduced to 1^3x

Answer 3

do you have to find the second derivative?
Possibly using the l'hospital's rule?

Answer 4

you now have an exponential term, so as x reaches infinity, the number approaches infinity. so the limit is infinity (or does not exist)

Answer 5

it'll be like 1^3*1, then 1^3*1000....the number just goes on forever with no limit

Answer 6

i see. thanks

Answer 7

no problem