And let's say my d sub tau of well, let me put it as a function of t because everything we're doing in the

I spit out f of 1, which is equal to 2 in that situation.

And you want to be very careful here.

However, in Big Theta world, this is also n².

The Maclaurin series representation out them the Macloren series representation.

The whole point of this video is to clarify the motivation for calling them even or odd functions.

In the case of a Maclaurin we're picking x equals zero, and it equals every derivative of this function.

X and y are not 0, then they're eliminated. This one is retained.

And its solution isn't a number, its solution is a function, or a set of functions, or a class of functions.

And if you've listened to a lot of my videos, you'd realize that it probably is what I consider to be the most amazing function in mathematics.

And in that domain, 2 is sitting there, you have 3 over there, pretty much you could input any real number into this function.

We might talk more about that later.

We may say like t.render( a, kw ).

The correct answer is that procedure 1 will terminate, procedure 2 will not terminate for all n, and procedure 3 will terminate.

So here is the definition.

Now again we will remove html markup with this parameter.

And we know that in the real world, everything isn't these nice continuous functions, so over the next couple of videos we're going to talk about functions that are a little bit more discontinuous than what you might be used to even in kind of a traditional calculus or traditional

Generally you say a .

I was going to write an x again.

It is mapping us from 2 to 8.

Now let's assume that we cut off the search at this depth, and we want to have an evaluation function, and the goal is for Pacman to eat all the food.

But reading this Python tuple stuff, that's really hard, so let's write a procedure to walk down one of these trees and print out everything in order.

I've actually given you most of this code.

So what's happening?

Whether it's video or text or music or voice, it's all numbers, it's all, underlying it, mathematical functions happening, and Lovelace said, Just because you're doing mathematical functions and symbols doesn't mean these things can't represent other things in the real world, such as music.

Not all even functions are going to be of this form here, where it's x raised to some even power, and not all odd functions are going to be.

Or let me just write it a little bit cleaner.

So you kind of group them all together as even functions.

This whole thing, by definition, this unit step function is zero until we get to c.

We have to pick a direction.

There's one last thing we forgot to do.

We have to hold everything else constant and take the derivative with respect to just one variable.

And a star is going to loop back on itself.

This is supposed to be a constant

And you sometimes wonder, well what was all of the hubbub about?

When I introduced you to the unit step function, I said, you know, this type of function, it's more exotic and a little unusual relative to what you've seen in just a traditional Calculus course, what you've seen in maybe your

And it keeps going in either direction.

Well, it's going to be the value of the Dirac delta function.

Here, when you take the subtraction, you're taking the one that had a derivative, now it doesn't.

I'm going to give you a start for how to write this procedure, and then you're going to finish it.

He also is not going to sell half of a ticket.

We've already seen our tracing functions where we can access the individual execution frames of a run.

Let's start with the first expression. This one over here doesn't depend on sigma at all.

And the answer is C.

At first, you might think, oh boy, this is complicated.