lim x goes to infinity of x!/x^x.

Question

Calculus 2 limit calculations

Answer 1

x! = x * (x-1) * (x-2) * (x-3) * . . .

x! = (x^2 - x) * (x-2) * (x-3) * . . .

x! = (x^3 - 3x^2 + 2x) * (x-3) * . . .

x! expanded will always be of the form x^x + ax^(x-1) + bx^(x-2) + cx^(x-3) + . . .  The leading exponent will always be x.  That is, the expansion- however far you take it, however big it becomes- will always start with x^x.

For the purposes of a limit, you'll end up with x^x / x^x = 1

I *think* the limit is 1.