When t is equal to infinity, what is x?

So we're going to evaluate this term right here from 0 to infinity.

So, even though we're familiar with only a few irrationals,

You have an infinite number of possibilities here and an infinite number of possibilities here.

The answer is 0.

So as x approaches infinity.

It includes negative 15.

The possibilities are endless here.

But the boundary stays.

Does anyone want to guess what it is?

I'm going to write it in quotes.

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

It's much more memorable.

Remember that the width of the confidence interval decreases with the n.

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And then an even bigger one by making the set of all the subsets of that one. And so on.

So what happens as this term, right here, goes to infinity?

And then you have to evaluate that from 0 to infinity.

And we're going to go all the way to infinity.

Its storage is functionally infinite.

And you can't really simplify this anymore.

I wrote a little bit bigger than I wanted to, but that's OK.

And an e to the minus googolplex is an even smaller number.

So let's see if we can simplify this.

And I hope you understand what I'm saying, right? e to an infinity negative number approaches 0, while e to an infinitely positive number is just infinity.

There's finite series, and infinite series.

We're going to have to take this whole thing and evaluate let's just say that y is the antiderivative and then evaluate it from infinity to 0.

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.

There's more. We just pointed out that the set of decimal numbers

Resolution is something that is far more limited.

So we're faced with this astounding conclusion

The possibilities of this tool are as infinite as YouTube itself.

I'm focusing so much not to make careless mistakes.

1 a minus s times e to the a minus st.

So if x with a infinity would go to zero because it is a constant

But anyway.

So in order to figure out which one of these this is, let's just think about what happens as x becomes infinitely large.

So anyway.

So let's do that.

And let me not forget our boundaries.

An Infinity

let me rewrite the whole thing.

This is what you approach as x approaches infinity.

They are constant with respect to t.

So minus this part.