Post #11?

Well we worked on the Taylor and Maclaurin Polynomial/Series something things.

Taylor:
Pn(x) = f(c) + F'(c)(x-c) + (f''(c)(x-c)^2)/2! + ... (f^n(c)(x-c)^n)/n!
*C is used b/c it is not centered a zero.

Maclaurin:
It is simply the same formula, but 0 replaces the c.
*This is one is centered at zero.

This will be a very short blog because....I don't understand this really.
I don't have my notebook..so I can't really think of problem. But I do know you follow the formula like you plug in c for the equation so that's the first term, then do + take the derivative and also put (x-c)

Can someone show me example pleassssse? I just really need an easy step by step for this.

11/7 post.

so this week in calc bc we finally quit learning the hard stuff in chapter nine, (like sequences and series) and moved on to something that i'm starting to understand better! thank you! haha.
we learned taylor polynomial and some other stuff. so this is the formula thing for it...

Pn(x) = f(c) + F'(c)(x-c) + (f''(c)(x-c)^2)/2! + ... (f^n(c)(x-c)^n)/n!

also we learned somehting called Macclaurin series. this uses the same formula, except everywhere you see c, you put 0. because Macclaurin's formula is centered at 0.

it was all-in-all a pretty simple week. you just follow that formula. i don't think i had any questions. let me just throw in a little something though to make this blog a little longer.

limit rules as n approaches infinity.
1. if top degree > bottom degree = +/- infinity.
2. if top degree < bottom degree = 0.
3. if top degree = bottom degree = divide leading coefficients.

yayyyyyyy :D

Post for 11/7

So this week in the wonderful world of Calculus BC: Taylor Polynomial and Approximations.

I would just like to say that I have absolutley no clue at all what these are or how you do them. So that is pretty much my question for the week.

After teaching Mu A practice I realized that I am kind of rusty with my derivatives.

So today's post will be about derivatives.

d/dx [uv] = uv' + vu'

d/dx [u/v] = (vu' - uv') / v^2

d/dx [sinu] = (cosu)(u')

d/dx [cosu] = -(sinu)(u')

d/dx [tanu] = (secu)^2(u')

d/dx [cotu] = -(cscu)^2(u')

d/dx [secu] = (secu)(tanu)(u')

d/dx [cscu] = -(cscu)(cotu)(u')

d/dx [ln(u)] = u' / u

d/dx [u] = (u)(u') / (u)

d/dx [e^u] = e^u * u'

One rule for derivative that the Mu A's weren't really getting was chain rule. I told that the way I remember it was to work from the outside in.

Peace Out,
Ryan

Yet another blog.

Let me just say that today I sat down and did all my homework. Rather attempted all my homework. I found myself terribly confused once you get to remainders and such. I know for a fact that I need help on that. However I do know how to find whatever degree polynomial functions.

So Taylor is the series your generating. it's given as:

Pn(x)=f(c) + F'(c)(x-c) + (f''(c)(x-c)^2)/2!...

C is going to be any number really, and you're just going to plug in the number to the original (they give you it) and then take the derivative and plug into the formula.

Now the difference between Maclaurin is that Maclaurin is centered at 0, meaning that your c is zero. so you're just going to start off by plugging in zero to the original the just taking the derivative and repeatedly plugging in the zero. And after approximating a value to the degree the problem it tells you to, you're get your answer (use this when you have like cos(1.1), or something you know you cant to without a calculator easily)


For stuff I DO NOT GET. I do not get how to find the remainder. Also, what do you do if you're approximating something and you find a pattern? like after the 4th term you get what you started with? Just a couple of questions. :DD