This formula is very similar to the formula for finding the coefficient of x k in a Maclaurin polynomial where the derivative is evaluated at 0. The coefficient of the term (x - 1) k in the Taylor polynomial is given by ![]() The second-order Taylor polynomial centered at 1 for the function f( x) = e x can be found by using a procedure similar to the procedure given in Lesson 24.2. The Taylor Polynomial of e x Centered at 1 Is called the nth-order Taylor polynomial for f centered at a.Įvery Maclaurin series, including those studied in Lesson 24.2, is a Taylor series centered at zero. The Taylor series is a power series that approximates the function f near x = a. ![]() Is called the Taylor series for f centered at a. Given a function f that has all its higher order derivatives, the series This lesson investigates how to find a series that approximates a function near x = a, where a is any real number. In Lesson 24.2 you found Maclaurin series that approximate functions near x = 0. ![]() Module 24 - Power Series - Lesson 3 Module 24 - Power Series
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