Taylor's Theorem by hdelgad2

Last crawled date: 3 years ago

This is Taylor's Theorem approximation created in Mathematica version 10. George Mason University Math 493 for Mathematics Through 3D Printing.
This project demonstrates Taylor’s theorem giving an approximation to the cosine function. The Taylor series is given by f(x)= ∑_(n=0) to ∞ cn (x-a)^n, where cn = f^n(a)/n!.
where f(x)=cos(x) and a=pi.
Using polynomials functionality to compute the nth degree, the nth degree is increased by even numbers which brings us to a better approximation.
Let x^n/n! , where n equals a positive even integer starting at n=0
cos⁡(x)=1-x^2/2!+x^4/4!-x^6/6!+x^8/8!-x^10/10!…
Note: For x^n/n! , where n equals a positive odd integer starting at n=1 will create an approximation to the sine function.