In this video I go over Question 6 of the Laboratory Project: Taylor Polynomials and this time look at an example on how to apply Taylor Polynomials to approximate the function f(x) = cos(x) centered at x = a = 0. This example involves determining the 8th degree polynomial and comparing it graphically with the 2nd, 4th, and 6th degree approximations. The first step in solving for the 8th degree Taylor Approximation is to take the derivatives up to the 8th derivative and solve each one for when x = a = 0. Doing so we can clearly see a pattern since the derivatives of cos(x) involve alternating sin(x) and cos(x) functions but with varying positive or negative signs. Since sin(0) = 0, I show that the odd terms, given the first term is considered even or zero, all vanish thus greatly simplifying the final formula. The 2nd, 4th, and 6th Taylor Approximations are all simply determined from the 8th degree Taylor Approximation since each successive iteration just adds a new term to the formula. Graphing the approximations all together with the function f(x) = cos(x) and centered about x = a = 0, I show that the approximations gets better and better for each successive iteration especially as the interval gets larger and larger. This is a very careful and detailed video showing how to approach and apply Taylor Polynomials in approximating a given function, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh49wGMItOOnDiBSnBg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/laboratory-project-taylor-polynomials-question-6-example
Related Videos:
Laboratory Project: Taylor Polynomials: Question 5: Proof:
Laboratory Project: Taylor Polynomials: Question 4: Approximating Square Roots:
Laboratory Project: Taylor Polynomials: Question 3: (x - a) Approximation Form:
Laboratory Project: Taylor Polynomials: Question 2: Approximation Accuracy:
Laboratory Project: Taylor Polynomials: Question 1: Quadratic Approximation: .
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I'll definitely keep an eye on your tutorials, even if I already know most of it , your explanations bring something fresh to Math.
Thanks! Yup, I started my channel because remembering all the different math stuff was getting tedious. So better way to remember and create a database for future reference than by creating my own Channel!!
I don't always finish off a Laboratory Project on Taylor Polynomials but when I do I usually end off with an example ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/laboratory-project-taylor-polynomials-question-6-example
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STOPGood post @mes