Fast approximation

And just as a reminder, a Taylor series is a polynomial approximation of a function.

And it's a pretty bad approximation, but at least it equals the function at this point.

Obviously, if we get far away, out here, this is a horrible approximation for the function.

At least if we stay pretty close to our chosen c, it's a decent approximation for the function.

I use as an approximation.

That'll be good for approximation.

But the approximation, even when it's centered at 0, actually equals the function when you take the infinite sum.

And you can say Sal, that is a horrible approximation it only approximate at the function at this point

Enable fast approximation when rendering images.

Line will draw a rough approximation.

So this is just an approximation.

How would be write the approximation?

So this is a better approximation.

So that's a first you can kind of all think of it as a 0 of order approximation of the function.

look something like this is all approximation.

So let's make the approximation of this.

0.39 is the approximation, so approximately 0.39.

And as you add more and more terms, you get a better and better approximation of your function and if you add an infinite number, it might actually converge to your function.

So if I just wanted this one term polynomial, what would be my best approximation for this function, at least at this point?

Even this approximation will be approximately normally distributed.

And this would be even a better approximation.

Your calculator will just give you an approximation.

So it would be a pretty bad approximation.

So what is the Taylor approximation, or the

One, you say, well this is an approximation.

Function

Function

Function

Function

Function

Function

Function...

Form is function. Form is function.

So that is my approximation, eye balling it like that.