Question

How do I find the limit `lim_(x->oo)e^(-x^2)`?

Answer 1

Examine the end behavior by taking arbitrarily large positive numbers for x, and noticing that `e^-(x^2)` approaches 0 the larger a value you take.. The limit is 0

Explanation:

First, note that `e^-(x^2) = 1/(e^(x^2)`. Now, begin plugging in positive values for x.

`x=1 -> 1/e`
`x=10 -> 1/e^100`
`x=100 -> 1/e^10000`

As can be noted intuitively, or shown via a calculator, or seen by graphing these values, as x increases, `e^-(x^2)=1/e^(x^2)` becomes smaller and smaller, approaching 0. Thus, as x approaches `oo`, the function approaches 0, making 0 the limit.