Question

How do you evaluate the limit `e^(-x)/x` as x approaches `oo`?

Answer 1

`lim_(x->oo)e^(-x)/x = 0`

Explanation:

To calculate this limit, we just recall that `a^(-b) = 1/a^b` and note that `lim_(x->oo)e^x=oo` and `lim_(x->oo)x = oo`, meaning `lim_(x->oo)xe^x = oo`. With those, we have

`lim_(x->oo)e^(-x)/x = lim_(x->oo)1/(xe^x) = 1/oo = 0`