MATH-M 212 Lecture Notes - Lecture 17: Function Approximation, Polynomial
Document Summary
Accuracy of approximations improved by using polynomials instead of lines. Find the polynomial that approximates the function: build polynomial around and begin with zero-degree polynomial known point constant function approximation of, for first degree, first derivatives should agree. Let: for second degree, second derivatives should agree. So: for third degree, third derivatives should agree. Definitions of taylor and maclaurin polynomials: taylor polynomial for at - if has derivatives at , then: And implied in first 2 terms (both : maclaurin polynomial for at , will be given -value on test/quiz. Find the maclaurin polynomial for with . o o o o o o o. Find the 4th taylor polynomial for centered at . o o o o o. Use the 4th maclaurin polynomial to approximate the value of : by calculator, Remainder of a taylor polynomial: exact value, approximate value, remainder, error.
