Question

Question #1feda

Answer 1

`e^4`

Explanation:

`lim_(x -> oo) ((x+3)/(x-1))^(x+3)`

I shall use `lim_(hrarroo)(1+1/h)^h = e`.

Let `t=x-1`, so that `x+3 = t+4` and we need to find

`lim_(trarroo) ((t+4)/t)^(t+4) = lim_(trarroo) (1+4/t)^t * lim_(trarroo) (1+4/t)^4`

`= lim_(trarroo) ((1+1/(t/4))^(t/4))^4 * 1^4`

`= lim_(trarroo) ((1+1/(t/4))^(t/4))^4`

`= (lim_(trarroo) (1+1/(t/4))^(t/4))^4`

`= e^4`