find-the-first-three-nonzero-terms-of-the-taylor-expansion-for-the-given-function-and-given-value-15

Name: find the first three nonzero terms of the taylor expansion for the given function and given value 15
Uploaded: 2019-07-18
Duration: 2 min 4 s
Channel: Numerade
Description: Find the first three nonzero terms of the Taylor expansion for the given function and given value of a. $$\sin x \quad\left(a=\frac{\pi}{3}\right)$$

Question

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

Doruk Isik · Accepted Answer

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&#x27;re going to be first. We&#x27;re gonna need the second day or two. So x, and we&#x27;re going to be I heard there was, which is meant to fight you. Co sign. Hi. Yeah, let&#x27;s have leg these Bunches that, um zero. So zero think zero here in this one that you&#x27;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&#x27;s old mummy Look degree three as f zero plus at time. Zero times X. What&#x27;s a double? 10 x squared over two pictorial waas. Triple time. Zero. Uh, excuse forward treaty. So let&#x27;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&#x27;s cute.

Sara Sasani · Answer

In this video, we find the 1st 4 nonsense terms off the Taylor series for the given function. A formal office Tillerson is generated by If he&#x27;s some off cape before 20 to Infinity. The case dirty off if zero divided by K Factorial, Times Explorer Kate Let&#x27;s first find if it F zero so we replace Exploit zero it. But if and we have, If zero is according to one, then we are supposed to find the first derivative off. If at zero, it is a call to tree on the second day, we give off. F zero is 1/4 12 on the 3rd 1 is a courtroom 60 based on their formula. The Taylor series Off the function one minus X over minus three. He&#x27;s been called to a zero plus if crime off zero kinds. Eggs, plus the second derivative off. If I had zero divided by two for courier kinds exist world class. The tear primitive octave at zero, divided by three factory all kinds excuse. After simply flying, we have the 1st 400 grams off the Taylor series for the given function. Hope you enjoyed watching this video, and thanks for watching

Hamilton Santhakumar · Answer

For this question, we begin by writing an expansion for sine X about X equals zero, and we know that it&#x27;s given by X minus X Cuba with three factorial plus extra the 5/5 trillion minus X to the seven or seven total and so on. What we need is sine x an expansion for sine X minus six plus excuse over three factory. So what we do is we just take the above our cities and then are these extra terms OK, so what? We Lewis, copy this power Siri&#x27;s and then subject X on ad X cubed over three factory. So you see that these stones get canceled. So what? We get this finally x cube. So the extra the five it extra the five divided by five factorial minus X to the 7/7 factorial and then the next time will be extra the 9/9 factory and so on. And that&#x27;s the publicity&#x27;s

Jin Yan Yeo · Answer

in this question first, that it&#x27;s the integrate tension t. So well, First, I don&#x27;t know what the tailor Siri&#x27;s like. A tendency is. So it iss a lot off terms, but we&#x27;re only interested in the 1st 3 terms. So we&#x27;re gonna integrate the 1st 3 terms from the Road of X. And we can do that by applying the change route to each off These three tells and again we are only interested in the 1st 3 times because we are only interested in the 4th 3 non zero terms so we can integrate them by applying a chain rule. So we increase increase the power off TV. I want anybody about a new power. We don&#x27;t substitute eggs into each of the T terms. Okay, not in all bound zero, because when he stops to do zero into any off the CI values, we get zero and on, except it&#x27;s a recognized it. When we integrate 10 gen x, we get lawn Cygan X, which is what we&#x27;re interested in here. Ultimately, we want to find the tailor Siris for lawn second X. So we can we know that lawn Siegen x iss. It is equal to integrating tendency from zero X and that is exactly what we&#x27;ve just done earlier. So the approximate detailer Siris for a long second X would be be, expect the expansion that was just derived audio.

Jaida L · Answer

so the Mekele in Syria&#x27;s generated by side of exes Sigma from n equals zero to infinitely negative went to the party end, but by two and plus one factorial times x the part of two in post one. This converges are negative. Infinity to infinity and the Siri&#x27;s generated by, um, the natural log of one plus X is sigma for men equals one to infinity Negative once a part of n minus one. But my Aunt Times X apartment, which converges on native 1 to 1. So again this Siri&#x27;s we&#x27;re here is equal son X and this Siri&#x27;s right here is natural log of one plus X. And so the Siri&#x27;s generated by F of X, which is just these two functions multiplied together, is going to equal Sigma an equal zero to infinity. Negative wants the part and divided by two in plus one factorial times X to the power to and plus one and then this multiplied by Sigma n equals zero n equals one Teoh infinity the negative wants the part of and minus 12 by two by end times X apartment. And so once reasonable fire we should get This is equal to x squared minus 1/2 x cubed +16 x Afford this convergence on the intersection of hold on X squared. So this is X squared. This Siri&#x27;s right here converges on the intersection of negative infinity to infinity and negative one toe one. So the actual interval convergence is negative ones toe one. Remember, this is going to be minus Doctor dog. And so the first terms are going to be represented right here. So X squared minus what happened? X cubed +16 x to the fourth and then the interval. Convergence is negative 1 to 1.

Problem

Find the first three nonzero terms of the Taylor …

Problem 13 Easy Difficulty

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

Answer

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

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

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Caleb E.

Samuel H.

Integration Review - Intro

Definite vs Indefinite

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Caleb E.

Samuel H.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus