This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 11.12 Applications of Taylor Polynomials Tables of integrals and trigonometric functions can be done with expansion of power series. Suppose that f(x) = the sum of its Taylor series at a: ) ( ) ( ) ( ) ! n n n f a f x x a n = = then the n th partial sum is the n th degree Taylor polynomial. ( ) ( ) 2 ( ) ( ) ( ) ! '( ) ''( ) ( ) ( ) ( ) ( ) ( ) 1! 2! ! ( ) ( ) ( ) n n i n i n n n n f a T x x a n f a f a f a f a x a x a x a n T f x as n so f x T x = = = + + + + L Polynomials are simple functions and can be manipulated without much difficulty. In Math 1550 you found a linear approximation for a function (tangent line approximation). In fact, the tangent line approximation is the 1st degree Taylor polynomial of the function. 1 ( ) ( ) ( ) '( )( ) L x T x f a f a x a = = + Derivatives of T n at a agree with those of f up to and including derivatives of order n. When we use a Taylor polynomial to at a agree with those of f up to and including derivatives of order n....
View
Full
Document
This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.
 Fall '08
 Estrada
 Polynomials, Integrals

Click to edit the document details