Visualizing Taylor polynomial approximations | AP Calculus BC | Khan Academy

Approximating e_ with a Taylor polynomial centered at x=3. In the video we find the first few terms of such a polynomial and graph it to see how close it gets to e_. Created by Sal Khan.

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

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[Goldbergfan]

With the testing for convergece stuff around 1:25, it sounds like you might be getting into a bit of Numerical Analysis. Awesome.

[lexinaut]

Well, this is very clear, and it's fascinating to watch the close convergences develop. Humbly, I must say, I find Taylor Series to be awe-inspiring. Modeling functions with infinite polynomials blows my mind out the door and into the next county. I suspect my mind could use some extra elastic proteins added that Taylor must have had in abundance in his rather incredible, plastic fantastic, and drastically insightful brain!

[harishli]

awesome please uploading visualization videos like this...

[lexinaut]

@LV07TSK Thanks! Glad you enjoyed the comments. I try to keep my sense of humor engaged in dealing with math. I wish there was an infinite polynomial breakfast cereal that would make the topic more accessible to the general public. Taylor polynomials definitely require mental physical fitness. I'd best get over to the neurotransmitter gym before I look them over again.

[horsethif]

You can also visualize this on Windows Calculator (graphing mode)

[abhishekarya]

Hey sal!!!!
can't u make a video on Gaussian integral...

[PBTech]

Can you do a video on the lagrange remainder and taylor's inequality?

[Waranle]

@MrTopa92 go to calculus playlist and ya will find them there "The Indefinite Integral or Anti-derivative "

[PCGamerPortal]

Do you have anything on parametrizations?

[erikmamet]

Hello ! I was wondering what the last term on the graph's expression was for 0((x-3)^6) : I know that it is a "negligeable" sign (or at least that is what it is called in french) but I do not see it's use in the taylor series. Could anyone help me out ?

[MrTopa]

@khanacademy could you make a video of a antiderivative because i'm having some trouble whit it and it would help me a lot (and sry about my English it's not my native language) thank you in advance

[joliettraveler]

If we look at each term except the first it looks like each one will be zero.  If x = 3, and each term other than the first has a factor of (x - 3) then why wouldn't they be zero?

[hellokat]

what's wrong with the Eng sub, it does not show up

[jpmorgan]

what's confusing: the graph of successive taylor terms looks great around the point of interest, but what about points further away? The approximation looks horrible out there! What gives?