Question

How do you find the limit of `(1+3/x)^(2x)` as x approaches negative infinity?

Answer 1

`e^6`

Explanation:

`L = lim_{x \to - \infty} \ (1+3/x)^(2x)`

let `1/p = 3/x, \qquad p = x/3`

`\implies L = lim_{p \to - \infty} \ (1+1/p)^(6p) = lim_{p \to - \infty} \ ((1+1/p)^(p))^6`

From well known limit:

`\implies L = e^6`