Question

limit x approaches to infinity (1+2/x)^x

Answer 1

hint : substitute x = 2t

Answer 2

@ganeshie8 can you message me how to solve this?

Answer 3

@dan815 or you mebby?

Answer 4

\[\large \lim \limits_{x\to \infty } \left(1 + \frac{2}{x}\right)^{x} = \lim \limits_{t\to \infty } \left(1 + \frac{2}{2t}\right)^{2t}\]

\[\large = \left(\lim \limits_{t\to \infty } \left(1 + \frac{1}{t}\right)^{t}\right)^{2}\]

\[\large = \left(e\right)^2\]

Answer 5

Anyone care to try finding this limit using an alternative method using logs and l'Hopital's Rule?