Error Bounds for Taylor Polynomial Approximations

Показать описание

JCCCmath

Рекомендации по теме

Комментарии

Thank you so much. This was clear and easy to follow. I was getting frustrated with the error term because I couldn't understand what c was and what f(c) was and why they were unknowns and why we were trying to find their max value. Everything online and in my textbook said the same thing; "This is the formula for the error term and this is how we will use it; do this and do that and move that around and take this out, and bam we have a value. Easy peasy!" But it didn't make any sense to me. The small explanations you did on the side as you wrote the formula made such a difference. If they didn't give me the whole picture, they gave me the first clue ("C is a mystery value. F(c) is unknown because if we had known it we wouldn't need to calculate the error."), from which I was able to track the next couple of clues easily ("Ah, okay, so F(c) is like a mysterious quantity we add to our approximation to reach the real value of F(b), and to make it more tangible and limit the worst case scenario to a number instead of leaving it lying in an infinite interval of numbers, we attempt to get the maximum value that this unknown F(c) can take.")
It's always good to know how something came to be and why it is that way and it doesn't hurt to repeat and re-explain something that might seem obvious because more often than not, at least for me, numbers all of a sudden can become vague and obscure instead of self-explanatory. And words help dispell that.

sarahbiebah

Very clear and organized presentation. Thank you very much.

gleon

How does he write like that?? Like that’s def backwards to him

ClaireBeard

Thank you very much indeed this is really easy to follow and well explained

MukelabaiSindila

Excellent explanation, sir, *Thank You!*

billwindsor

Thanks sir, nicely explained, clear and also in a very creative way :)

Gothfen

Great video! Is there an additional video that finishes the problem? Thanks!

fredross

I just dont understand why the c is in between a and x0 (the point of our intrest) given that we're intrested in x0 then f^(n+1)(x) is supposed to be evaluated at x0 ...and other points of x are simply irrelavent . I understand that error bound should be as large as it can be by taking into account the worst case scenario and this is how we can bound it ..but x is supposed to be between a and x0 instead of c=x0 which is where we wanna know value of our approximation .
What am i missing here?

dhiaelhakrouabah

What if I was trying to estimate f(1/17)?

fahrenheit

Please tell me how can i make video like this

syedatif

Error Bounds for Taylor Polynomial Approximations

Error Bounds for Taylor Polynomial Approximations

Taylor's Remainder Theorem

Taylor polynomial remainder (part 1) | Series | AP Calculus BC | Khan Academy

Lagrange Error Bound to Find Error when using Taylor Polynomials

Taylor Polynomials - Video 3 - Error Bound

📚 Finding the Remainder of a Taylor Polynomial – Example Using Taylor’s Remainder Theorem 📚...

Taylor Polynomials - Video 4 - Using the Error Bound

Math 151: Taylor Polynomials and Error Bounds

Find the error bound for a Taylor polynomial

Calculus II: Error in Taylor Polynomials

A Swift Introduction to Lagrange Error Bounds (Taylor Series) | #some3

Math 151: Another example with Taylor Polynomials and Error Bounds

Taylor's Theorem with Remainder

Calculus 2 Lecture 9.9: Approximation of Functions by Taylor Polynomials

Calculus 2 - Taylor Polynomials and Error Bounds - Practice Problem

Find an error bound on e^x, fourth degree Taylor polynomial, illustrated with graphs!

Calculus BC – 10.12 Lagrange Error Bound

Taylor polynomial remainder (part 2) | Series | AP Calculus BC | Khan Academy

How to Use Taylor's Theorem to Bound the Error in a Taylor Polynomial Approximation

Error bounds on Taylor polynomial approximations - Part 1

AP Calculus Section 9.3 Lagrange Error Bound or Taylor's Theorem Remainder

Error Bound of Taylor Series Warm Up

Taylor Polynomials & Maclaurin Polynomials With Approximations

Error Bounds for Taylor polynomial for e^1/2