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

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

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

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.

02:47

Find the Taylor polynomial…

01:43

02:51

01:54

problem. Three, we want to find a tighter point. Romeo's off orders. There are 23 So here is a technician on. Just copy that. Okay, so he's zero axe this? Ah, just, uh a right What is f a 18 with one. So peter act, it's just low on one is zero. So p p zero x and you are next this zero plus, uh, prime a times X minus. A might have primate is just well, the next his axe over when the racks, right, primarily. Just one over axe. So one away Times ducks minus a when they is one. So he won't actually is sterile. You for that X minus? What right that people are next and just compute p two x you two x is X minus one. That's, oh, take a nutter directive. That's a minus. When that's why times thanks minus a squared, divided by to work toward so that his minus one over two x minus one square that that's the third term here, right? Pito access does this. There's no this terms here because Peter actually is up to axe to the square. Right? And peace reacts. He's reacts. Have taken under that's Ah two or next to the three. Actually, it's one. So that's just us to be guided by directorial Times X minus one kill. So it is just one, sir X minus one Q. That's a first term here as before, sir, there's no sort of saying they're right.

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