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Find the first five Taylor polynomials for $f(x)=\sin x$ centered at $0 .$ Graph them on the interval $[-4,4]$ and comment on how well they approximate $f .$

$T_{5}$ is a better approximation than $T_{3}$ and $T_{4}$ which in turn are a better approximation than $T_{2}$ and $T_{1}$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Missouri State University

Campbell University

Harvey Mudd College

Idaho State University

Lectures

04:40

In mathematics, a derivati…

30:01

In mathematics, the deriva…

03:17

Find the 8 th-degree Taylo…

07:28

(a) Find the Taylor polyno…

02:18

Find the Taylor polynomial…

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For the functions defined …

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In the following exercises…

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08:07

03:04

03:23

01:32

Use a computer algebra sys…

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06:24

a. Find the nth-order Tayl…

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Suppose $f(0)=1, f^{\prime…

in this problem. Where else to find 83 Taylor Taylor pulling a lettuce center that zero matter Brooks weighs reflection. Nipple prices, coastline. So, um, you know Francisco sine X several permits and primal practice with predictive sign eights that double primer facts would be negative of Kansai necks. A triple prom X would be sine X and, uh, for their talk. Thanks would because I So we're started. What's co sign Next Know we're back of co signing, so we know that this is cycle ending with a link. Oh, four. So let's see what the function on David is that the even points I have zero would be one. That primal zero would be zero that double prime zero make or people prime zero is zero or they're a team of zero would be one and promises command again. Repeat itself. So we can say that Debra till zero for being zero at 6 30 in zero will be nicked. One of seven zero will be zero and age of zero will be one so we can write together pulling well that we're looking for as I have zero plus the prime zero times explaining zero plus at double Promise, Your Excellency your spray or do pictorial wasa trip of prime zero times X minus their acute over three factorial. What's that? That does. And 8 30 till zero. Chance. Explain it. Zero to the eight power. Gratifying as you can see, if you have a bit of 0070 even Paul. Oh, powers of zero. And even powers are either all Attila or night. So from this we find the 80 people Taylor on a meal, the approximation of proton X at 10 to be one minus expert over to factorial plus export over four factorial minus +66 over six factorial plus x a over age pictorial. No, um for me take terms up to the second power of legs. This is T too. And a before power is t 46 Power 66 over terms our teeth. Hey! So as we included more than war comes, we got more and more close to the rial. Functioning approximation actually gets better and better, so we can say 98. So, being good, all the terms will be more include NT six and this would be more prudent before and this will be more 22

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