Question

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

Answer 1

I would rewrite to use `lim_(trarroo)(1+1/t)^t = e` and continuity of the exponential function.

Explanation:

`(1-2/x)^x = (1-1/(x/2))^x = ((1-1/(x/2))^(x/2))^2`

As `xrarr00`, we have `x/2rarroo`, so `((1-1/(x/2))^(x/2))^2rarr e^2`