Replaced by this fantasy.

It's not creating a new list it's mutating the old list.

KB OK, swap over positions.

Let me put the Laplace transform of and I'm also going to the sides.

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Supersede

It's equal to some function of x and y.

Or, we could say, let me just write it the other way.

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And the worst thing? It's all done in secret.

Now, since we want to apply this to an integral, maybe

Now we know what g of 3 is equal to.

Right? Because that's not the way the world works.

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So what is this equal to?

That means the heap property isn't satisfied but all we have to do to fix it is we just swap the value in the left child and i.

Now I can go through and do the same for the length calls

We made the substitution that v is equal to y over x.

let's substitute 42 into our original equation

We have 7 minus 10 5.

But we could put an x in here.

This option, pplus goes to P, corresponds to picking just one.

Do you want to replace it?

And if you replace this expression everywhere, where you see an x, right?

F to replace forward

And now, if we wanted this in terms of x.

Using what I described in the previous slide what we're just talking about, you can actually patch this up by moving the 50 around doing some various swaps.

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Simple game quest.

In a function definition, it basically takes all the parameters and puts them into a tuple.

Well, if I can algebraically manipulate this right side of this equation, so that I can actually rewrite it.

Using these rules, if I start with sentence,

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All right.

This expression is just another way of writing this expression.

A trigger and the system tips over,

So f of 5 is equal to 5 plus 3 times g of 5, right?

So the fourth element will now be this text

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(Laughter) That's how we process information.

And that's not what we have up here.

And then we have our outer integral. x goes from 0 to 1. dx.