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The Taylor polynomial of order 2 generated by a twice-differentiable function $f(x)$ at $x=a$ is called the quadratic approximation of $f$ at $x=a .$ In Exercises $41-46,$ find the(a) linearization (Taylor polynomial of order 1 ) and (b) quadratic approximation of $f$ at $x=0$$$f(x)=\ln (\cos x)$$

$$L(x)=0 \text { and } Q(x)=-\frac{x^{2}}{2 !}$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Campbell University

University of Nottingham

Idaho State University

Lectures

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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.

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

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Quadratic Approximations T…

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The Taylor polynomial of o…

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Here are of it is el costs, so f dash of it. You can write it as minus in x in minus 10 point so because the length was f dash of x will be 1 by cos into minus sine x. Minus sine by cos is minus 10 s. E and f. Double dash of x will be take the derivative minus 10. Is that will be minus of c square now and from 0, then will be 0 and f dash of 0 also will be 0 and f. Double dash of 0 will be c. Square of 0 is 1 and there is a sin here, so that will be minus 1. Now that e l o s o 0 and q f s equal to minus square by 2 point, i hope you understood the problem. Thank you.

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