Compute the limit of x/exp(x) when x approaches positive infinite?

From: Daniel Mark (liudanyu_at_gmail.com)
Date: 08/10/04 

Date: 9 Aug 2004 19:22:34 -0700

Hello all:

I want to compute the limit of formula x/exp(x) when x approaches positive
infinite.

I use the following procedure to prove that it is 0.
Is this method correct?

1> 0 <= x/exp(x) <= x/x^2 = 1/x when x approaches positive infinite.

2> 0 <= x/exp(x) <= 1/x = 0 when x approaches positive infinite.

3> therefore, x/exp(x) ==> 0

thank you
-Daniel