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Find the Taylor polynomials of orders $0,1,2,$ and 3 generated by $f$ at $a$.$$f(x)=\sqrt{x}, \quad a=4$$

$$P_{3}(x)=2+\frac{(x-4)}{4}-\frac{(x-4)^{2}}{64}+\frac{(x-4)^{3}}{512}$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

03:09

Find the Taylor polynomial…

02:24

02:51

02:40

problem night. I was doing the finance hater party. No meals. And here's the definition. Just use this formula. Okay? Has to give the F axis cortex prime axes, uh, two squared axe. No one. Pride, pride, lax. It's, uh ah. Or thanks to the minus three years, minus 55 Prime Max. Oh, man. Or for sorry. Yeah, I know are for It's us. We were eight. Thanks. Do you mind us? I've got to. Okay, let's give u P zero acts is just, uh when a is for so four. What is that for it too, right? And he went next is two plus something. Times X minus for All right. That is, uh, when ducks before. So that's 4144 right second floor Yet that the second term is one or four times X minus four and Pito axe. His people are next. This copy it and plus some saying times X minus four square. So that's, uh, one, uh, the next. It's equal to floor. So that's two to assert a minus one over 32 divided by two. So you wonder where 64 am I correct? It's just that in terms years at 11 Niner. Six before here and peace reacts. It's ah P two x plus something times X minus for to the Cube. So that's one actually before. So that's Ah, 16 times. That's a 32 time's A And here, this three and tax relief factorial. That's the stakes. So that's a 16 times 32 Ah one. There were 512 right? Yeah, one or 512 eso.

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