Question

Find the limit:
lim (x+1)^x / (x)^x as x->+infinity

Answer 1

e

Answer 2

lim (x+1)^x/x^x= lim [(x+1)/x]^x= lim [x/x + 1/x]^x= lim (1 + 1/x)^x

as x-> infinity, 1/x= 0, therefore lim (1 +1/x)^x = (1 + 0) ^infinity= 1^infinity = 1
since 1 power to anything always equals 1

Answer 3

i think you missed something but according to my calculations the answer is e

Answer 4

you actually cannot eliminate 1/x as it is not seperate

Answer 5

the answer to 1.0000001^1000000000000 equals 2.792 , try it

Answer 6

TI-89 also shown e, but at least you should show him how you solved this

Answer 7

as lim (x+1)^x / (x)^x as x->+infinity becomes inf/inf form as x goes to inf so we use L hopitles rule but the derivative still does not give us th required results as it too remains inf / inf so we use series expansion which is
e+ e/2x +11e/24x^2.....
as the terms with x in denominator get 0 as x->inf so we are left with e