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

$$P_{3}(x)=\frac{1}{2}-\frac{1}{4} x+\frac{1}{8} x^{2}-\frac{1}{16} x^{3}$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Missouri State University

Campbell University

University of Nottingham

Idaho State University

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.

02:40

Find the Taylor polynomial…

02:51

01:54

01:43

For the function f of x, equal to 1 over x plus 2 f, 0 is equal to 1. Half first doatie is equal to negative 1 over x, plus 2 square and first date of 0 is equal to negative 1 over 2 square. Second, derivative is equal to 2 over x plus 2 to the power. The second to at 0, is equal to 2 over 2 cube, which is also equal to 11. Over 2 square. Third derivative is equal to negative 2 times 3 x plus 2 to the power 4 third to at 0 is equal to negative 2 times 3 over 2 to the power 4, which is equal to negative 3 over 2 to the power 3. Then we have the tale phenomena of all that 0 is 1. Half out of 1 is 1 half minus 1. Over 4 times x of the 2 is 1 half minus 1 over 4 x plus 1 over 4 times x, squared over 2. Other 3 is 1 half minus 1 over 4 x plus here. This is x squared over 8 minus 3 times over 2 cube times x, cube over 3 factorial, which is equal to here. This is equal to x, cube over 2 to the power 4.

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