Question

How do you find the limit of `(1 + (1/x))^(x/6)` as x approaches infinity?

Answer 1

`e^(1/6)`

Explanation:

`lim_(xrarroo)(1+1/x)^x = e`

and

`(1_1/x)^(x/6) = ((1+1/x)^x)^(1/6)`

So,

`lim_(xrarroo)(1_1/x)^(x/6) = lim_(xrarroo)((1+1/x)^x)^(1/6)`

`= (lim_(xrarroo)(1+1/x)^x)^(1/6)`

`= e^(1/6)`