ch11s12 - 11.12 Applications of Taylor Polynomials Tables...

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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: ) 0 () ( ) ! n n n fa fx x a n = = then the n th partial sum is the n th degree Taylor polynomial. 0 2 ( ) ! '( ) ''( ) ( ) ( ) 1! 2! ! n n i n i n n nn Tx n f a xa n Tf x a s n s o 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 ' ( ) Lx 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 . When we use a Taylor polynomial to approximate a function, how good is the approximation? How large do we need to make to be within the desired accuracy? The answer is the magnitude of the remainder: Rx fx Tx .
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.

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ch11s12 - 11.12 Applications of Taylor Polynomials Tables...

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