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Find the Taylor polynomials of orders $0,1,2,$ and 3 generated by $f$ at $a$.$$f(x)=\sin x, \quad a=0$$

$$\begin{array}{|l|c|r|c|}\hline P_{0} & P_{1} & P_{2} & P_{3} \\\hline 0 & x & x & x-\frac{x^{3}}{31} \\\hline\end{array}$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

01:59

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

14:11

In mathematics, the partial sums of a series are the sums of all terms of the series except possibly the first and last.

01:26

Find the Taylor polynomial…

02:20

04:48

02:40

01:54

02:24

For the function f x, equal to sine x, we have f, 0 is equal to 0. Derivative is equal to cosine x. Second, derivative is negative sine x. Third derivative is equal to negative cosine of x, so the half this is equal to 1 and second derivative. At 0 is equal to 0. Third derivative at 0 is equal to 91. To the tail of monomial. Of outer 0 is 0 onto 1, is equal to x. Over 2 is equal to x. Of the 3, is equal to x, minus x, cube over 3 factorial.

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