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

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

The chain rule, derivative of cosine is minus sign.

Transform symlinks

This expression is just another way of writing this expression.

But we can figure out what h of 10 is pretty easily.

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

Do you want to replace it?

Well you go back to the definition.

So it's f of 0 is 1.

And now we can use this, which we proved several videos ago, to resubstitute it and get it in terms of the Laplace

So C is equal to 6.

And we got g of 3 equals 7.

We could do no correction at all we have to consider that as one of the possibilities.

Well, let's do the same idea.

This is equal to 3 times 5, 3 times 5.

What that means because there's a little triangle here and we're trying see whether or not it's 3 colorable.

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

All right.

So this is the same thing as 9.1 times 3.2, and then I'm going to re associate, so I'm going to do these first.

Now, we compare the number of 6s with the number of 5s, and there aren't enough.

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.

You just get a 1.

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.

There's no trick to it.

What do I produce?

Everywhere that we saw an x, we will now replace it with a z.

Supersede

So I'm going to do over 2 times 2.5 times 10 to the negative 2 times 10 to the ninth.

That's equivalent to the absolute value for 5.

Here I've taken our expression grammar from before and updated it with a new rewrite rule.

And then from F, there is connection to D and G and those were already in the graph.

If you press the Replacebutton, the text you entered above is searched for within the document and any occurrence is replaced with the replacement text.

And so we get c2 is equal to 5 2.

Simple game quest.

Now we know what g of 3 is equal to.

Do you really want to supersede this article?

Because we were able to write it as a function of y divided by x.

In each square, we calculate the average color.

We have 7 minus 10 5.

We only have 1 replacement rule for subject.

That is the same as saying that the old salary was the new salary minus 10,000.

So let's use this one, it seems a little bit, marginally simpler.

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

Laplace transform of e to the at.