Plus b c i plus b c i.

So ac.

N dot L. The other idea is to make these narrower curves be higher, giving them roughly the same volume at 3D. This idea is captured in the last term.

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Or, if we add these two middle terms, you have fh times x, plus add these two terms fj plus gh x.

And, I'll come back and say more about this later.

So fn prime of x times the second function, g n of y, plus the first function, fn of x, times the derivative of the second function.

So let's take the x terms, since we get x squared minus 2x plus something to complete the square later on.

And then finally, another generalization.

Many faces will be contrite on that day,

Many a face will be disgraced on that day.

Faces on that day humbled,

Faces on that Day shall be downcast,

Some faces, that Day, will be humiliated (in the Hell fire, i.e. the faces of all disbelievers, Jews and Christians, etc.).

Faces on that Day will be shamed.

Some faces that Day shall be downcast with fear,

On that day (many) faces will be downcast,

Some faces on that day will be humbled,

On that Day faces shall be humbled,

Some faces, that Day, will be humbled,

On that day the faces of some people will be humbly cast down,

(Some) faces on that day shall be downcast,

On that Day, there shall be downcast faces,

Some faces, that Day, will be humiliated,

Write your name in the top right corner followed by birth date and social security number.

And he said, I'm not a psychopath.

So the second derivative, that's r squared times e to the rx, plus 5 times the first derivative, so that's 5re to the rx, plus 6 times our function 6 times e to the rx is equal to 0.

This is going to be equal to a constant over this denominator, over x minus 2, plus and this is a little different than what you were going to see, what you saw in the last video plus an x term, some coefficient times an x term, plus c, so bx plus c, over this. x squared plus 2x plus 4.

Important to realize, that, look.

What that means is there must be a moderating effect.

So y prime of 0, minus now we lower the degree one more minus s, times this is an s times y prime prime of 0.

And let me pick a good color here.

If we see a notch, then we simply have in our Pastry that we're not and then the contents that are being.

Who? Daniel's benefactor.

All this meant, when I wrote these parentheses times next to each other, I'm just going to multiply this expression times this expression times this expression.

The patients learn to do this themselves

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Transform of y, right, that's what we want to get to, is going to be s to the fourth times the Laplace Transform of y now every other term is going to have a minus in front of it minus lower the degree on the s minus s to the third.

And I'm going to do that in orange.

So that's our new real part.

We're just multiplying the corresponding terms, the third term times the third term, the second term times the second term, the first term times the first term.

And a crowd of the later.

And a large group from the latter.

and a throng of the later folk.