Lagrange Error Bound

Learn how to use Lagrange Error Bound and to apply it so that you can get a 5 on the AP Calculus Exam.

[oscarortega]

the taylor series for sin(x) to the third degree is x - (x^3/3!) not just x- (x^3/3)

[simonstead]

Your handwriting is absolutely fine, and you don't write anything down that you don't say out loud. Props!

[jextejt]

Just a quick note about the 3rd degree Taylor Polynomial for sin(x) should be x - (x^3/3!) or x - (x^3/6). A small error here, but it might be of concern to a student just starting out with these sorts of things.

[JaganDoodala]

This was excellently explained, and the video was incredibly precise! Thank you so much for your time!!!

[onice]

the confusion that i have dealt with for the last week finally makes sense! thank you so much!

[stellaveazey]

thank you so much! figuring this out has been very frustrating, but you explained it very well.

[DevinGagnon]

This is the best I have ever heard it explained, thanks so much.

[AlexSchendel]

Thanks! I finally understand how to use the formula I wrote down :)

[ramka]

How to find out sin(0.1)?
Is 0.1 in degrees or radians??
Please explain.

[pixelmine]

Watching this day of the exam because i suck at this 👊❤ tysm

[alexluwees]

How do you find the x that maximizes that function ? What if for example you had the 4th polyn of sinx, that means that 5th power of sinx would be cosx.. Then your max value would be 0 since (sin0 = 1). but "a" would be also zero, so now you have cos(0)/6! * (0-0) which is zero.
What am I doing wrong ?

[DynamicRoulett]

it may sound dumb but how come sin x is maximized when x is 0.1?

[leoz]

Good video, quick correction, the third degree for sin in taylor has a factorial in the denominator, no big deal, thank you again

[trm]

In books and other explanations I've seen they max sin t=1... not sin (0.1) ignoring the interval [0, 0.1]. I think your explanation makes more sense but who is correct?

[arunvenkit]

Thanks so much, this helped like crazy!!!

[MakExITxHaPpEN]

Thanks this made everything clearer!!!

[evanalmonte]

My question is, Would the error be greatest at x=.1 since the Taylor polynomial is centered around 0?

[onlyfrickinletters]

"Learn how to use Lagrange Error Bound and to apply it so that you can get a 5 on the AP Calculus Exam."
Darn! I wanted to learn about Taylor polynomials because they will be useful in life! /sarcasm

[kevinhu]

Where did he get (0.1) for the last step?

[MrRenanwill]

Lagrange Polynomial is not the Taylor Polynomial. Change the name of the title (and description) to "Taylor error bound" or something like this.