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Find the Taylor series generated by $f$ at $x=a$.$$f(x)=x^{4}+x^{2}+1, \quad a=-2$$

$$f(x)=21-36(x+2)+25(x+2)^{2}-8(x+2)^{3}+(x+2)^{4}$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Campbell University

Oregon State University

Harvey Mudd College

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.

01:44

Find the Taylor series gen…

01:06

01:45

00:45

a problem. 27 on the final state of serious, uh, here the definition of tender Serious. So that's computer frying, Ryan. Max. These four times extra que Thus two X right, So have Prime Prime Max is 12 actors square for sex. Primex. It's 34 x. The five time fired Max is 24 So and the others are all zeroes when this greater than four. So So let's thank you. And when a CZ minus two this term ists extinct has four plus one. So is 21. The fact is equals two 21. Thus, uh, when Hey, it's equal to minus two. His term is, uh ah 32 plus two minus 36 minus 36 and x plus two. Right And selectorial Here's, uh, forgave us too. So that's a 50. So that becomes 25 time sex, My express to square and trust this term here 2040 buddy. Bye, sweetie. Victoria, that's a four and the luster 34 divided by 24 hours. That's why X thus, too. Oh, here's a cube. The force. But here's the story. Terrorist 21 minus 36 25 by just eight years minus a one year, some minor say yet. Oh, actives even minus two. So it has a 48 and derided by six. So that's a so sorry. Here's the correct answer.

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