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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$$$f(x)=e^{\sin x}$$

$$L(x)=1+x \text { and } Q(x)=1+x+\frac{x^{2}}{2 !}$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

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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.

01:22

Quadratic Approximations T…

02:38

01:07

01:11

The Taylor polynomial of o…

01:21

03:27

01:30

01:49

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