This is what you approach as x approaches infinity.

Well as we approach infinity, e to the infinity just gets bigger and bigger and bigger, right?

So when we evaluated in infinity, as we approach infinity, e to the minus infinity approaches 0. f of infinity now this is an interesting question. f of infinity I don't know.

So this number becomes really huge as you approach positive or negative infinity.

But we can think about, what does this approach as x approaches positive or negative infinity.

infinity

Infinity

Only if s is greater than zero, when you get a minus infinity here does this approach zero.

An Infinity

So that is equal to e to the minus st, f of t, evaluated from 0 to infinity, or as we approach infinity, plus s times the integral from 0 to infinity of e to the minus st, f of t, dt.

0 to infinity.

A approaches infinity.

This was infinity.

So as x approaches infinity, or x approaches negative infinity.

As x goes to infinity, this expression goes to negative infinity. The exponential of negative infinity converges to 0.

like the Infinity Mushroom.

From 0 to infinity.

You're never at infinity.

What's sine of infinity?

Let's see, infinity, right?

Well x is, you know, infinity minus any constant is still going to be infinity, or if the limit is t approaches infinity, x is still going to be infinity here.

limit to infinity and it doesn't come to a finite number, the limit doesn't approach anything, that means that k the improper integral diverges.

Approach me.

One approach and this approach is super slow.

Once again, infinity is important.

It pops up to infinity.

All the way to infinity

So as x approaches infinity.

I mean, we could put it from minus infinity to infinity, it doesn't matter.

So as you approach positive or negative infinity, this equation is approximately equal to the plus or minus square root of 4 over 9x squared.

Now, both of these go to infinity, but this goes twice as high to infinity.

Taking the integral of this thing from minus infinity to infinity, since this thing is this thing, it should be the same thing as taking the integral of this thing from minus infinity to infinity.

Anyway, integral from 0 to infinity.

So that's this evaluated at infinity.

I said from zero to infinity.

The limit as n approaches infinity.

Manhattan no longer spreads its infinity.

And I'll give you several choices for x µ, x 0, x infinity, or x infinity.

You also do it for infinity, because infinity really isn't a normal number, so to speak.

We'd have to go from minus infinity to plus infinity to really get a 100 percent.

Because obviously you can't evaluate infinity, but you could take the limit as something approaches infinity.

The approach worked.

Approach the cow.

5 00 Approach

And we only care from zero to infinity, so I'll only do it from zero to infinity.