Question

How do you find the limit of `e^(x-x^2)` as `x->oo`?

Answer 1

`lim_(x rarr oo) e^(x-x^2) = 0`

Explanation:

This is not a vigorous proof but should be convincing enough for most college maths:

We have `e^(x-x^2) = e^(x(1-x))`

As `x rarr oo` then `1-x ~~ -x => x(1-x) ~~ (x)(-x) = -x^2`
So, As `x rarr oo` then `e^(x(1-x)) ~~e^(-x^2) rarr 0`

Hence, `lim_(x rarr oo) e^(x-x^2) = 0`