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Find the first three nonzero terms of the Taylor expansion for the given function and given value of a. $$\sin x \quad\left(a=\frac{\pi}{3}\right)$$

$f(x)=\frac{1}{2}\left[\sqrt{3}+\left(x-\frac{\pi}{3}\right)-\frac{\sqrt{3}}{2}\left(x-\frac{\pi}{3}\right)^{2}-\cdots\right]$

Calculus 2 / BC

Chapter 30

Expansion of Functions in Series

Section 5

Taylor Series

Series

Missouri State University

Harvey Mudd College

Baylor University

University of Nottingham

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Find the Taylor polynomial…

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Use power series operation…

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Integrate the first three …

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Use the definition of a Ta…

in this problem. We are us, too. Used teller colonials off the re tree, which a center for bait have props. Made the function signed by excessive Dimitri being holding a exit cell. We're going to be first. We're gonna need the second day or two. So x, and we're going to be I heard there was, which is meant to fight you. Co sign. Hi. Yeah, let's have leg these Bunches that, um zero. So zero think zero here in this one that you're zero a perm. Zero will be o R a double prime zero will be zero and a triple time. Zero negative. Fine. Here. Um, so Taylor's old mummy Look degree three as f zero plus at time. Zero times X. What's a double? 10 x squared over two pictorial waas. Triple time. Zero. Uh, excuse forward treaty. So let's just let these values, um, eggs. Zero plus buy eggs plus zero plus. Next, You, um, execute over six. So it and this is by eggs minus pi You over six. That's cute.

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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