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Power, Taylor and Maclaurin Series

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1 Power, Taylor and Maclaurin Series
Chapter 2 Power, Taylor and Maclaurin Series Lectures 8 & 9 : Taylor polynomials and approximations Find polynomial approximations of elementary functions and compare them with the elementary functions. Find Taylor and Maclaurin polynomial approximations of elementary functions. Use the remainder of a Taylor polynomial. Calculus for engineers MATH Level 3 Haykel MAROUANI Office F093

2 Calculus for engineers
Polynomial Approximations of Elementary Functions The goal is to show how polynomial functions can be used as approximations for other elementary functions. To find a polynomial function P that approximates another function f begin by choosing a number in the domain of at which and have the same value. That is, P(c) = f(c) . The approximating polynomial is said to be expanded about c or centered at c. Calculus for engineers MATH Level 3 Haykel MAROUANI Office F093

3 Calculus for engineers
Example 1 Calculus for engineers MATH Level 3 Haykel MAROUANI Office F093

4 Calculus for engineers
Taylor and Maclaurin Polynomials Example 2 Calculus for engineers MATH Level 3 Haykel MAROUANI Office F093

5 Calculus for engineers
MATH Level 3 Haykel MAROUANI Office F093

6 Calculus for engineers
Remainder of a Taylor Polynomial An approximation technique is of little value without some idea of its accuracy. To measure the accuracy of approximating a function value f(x) by the Taylor polynomial Pn(x) we use the concept of a remainder Rn(x) Calculus for engineers MATH Level 3 Haykel MAROUANI Office F093

7 Calculus for engineers
Example 3 Calculus for engineers MATH Level 3 Haykel MAROUANI Office F093

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