01spex3 - Math 222, Exam III, March 30, 2001 Answers I. (30...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Answers I. (30 points.) Complete the following paragraph by writing in the correct formulas. The Taylor series of a function f ( x ) about the point a is the infinite series X k =0 f ( k ) ( a )( x - a ) k k ! It may be used to compute f ( x ) when x is suFciently close to a . The n th degree Taylor polynomial of f ( x ) about the point a is the polynomial f n ( x ) of degree n which best approximates f ( x ) for x near a . It is f n ( x ) = n X k =0 f ( k ) ( a )( x - a ) k k ! The n th remainder (error) is defined by f ( x ) = f n ( x ) + R n ( x,a ) . Three formulas for the remainder are R n ( x,a ) = X k = n +1 f ( k ) ( a )( x - a ) k k ! R n ( x,a ) = Z x a ( x - t ) n n ! f ( n +1) ( t ) dt and R n ( x,a ) = f ( n +1) ( c )( x - a ) n +1 ( n + 1)! for some number c with a < c < x or x < c < a . The last is called Lagrange’s formula for the remainder. 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

01spex3 - Math 222, Exam III, March 30, 2001 Answers I. (30...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online