find-the-first-three-nonzero-terms-of-the-taylor-expansion-for-the-given-function-and-given-value-14

Name: find the first three nonzero terms of the taylor expansion for the given function and given value 14
Uploaded: 2019-07-08
Duration: 32 s
Channel: Numerade
Description: Find the first three nonzero terms of the Taylor expansion for the given function and given value of a. $$\cos x \quad\left(a=\frac{\pi}{4}\right)$$

Question

Find the first three nonzero terms of the Taylor expansion for the given function and given value of a. $$\cos x \quad\left(a=\frac{\pi}{4}\right)$$

Wen Zheng · Accepted Answer

So for the function, coz I have scarred artifacts. Plus, you know him no sign of blacks. MacLaurin series That&#x27;s Marty exist because through a tive off square, two backs at the point axial material that&#x27;s not exist.

Wen Zheng · Answer

the problem is used the definition off Attila Siri&#x27;s to find that the first of Horn and Ciro terms of the Siri&#x27;s or after back centered at secure ouali off, eh? So first we can&#x27;t relight, consign, exploit us call Sign to Max off, Juan Over, too. And then Terra Siri&#x27;s off Assign axe this some from Cyril Unity back to one to the power and counts ax to two. Aw, for children. Tardio. So we have assigned to Max. Is there going to some from zero to twenty? I think you want to end house to Max with the power off to over to him. A cardio prevention. It&#x27;s the control. What is it? A Syria lotuses one minus one. This is two ax squat. On the other hand, there&#x27;s they wanted to. This is two acts to the public or over, or factorial and minus two acts to the power of six over six Factorial. The chatterbox is equal to one minus X Lawyer Moss. Two acts to the power of four. Four factorial comes too wyness too. Thanks. I have a six over six factorial camps too. It was the first foreign and there were terms. Are this for terms

Ryan Williams · Answer

to start here. We&#x27;re gonna look at the power Siri&#x27;s representation for the co sign of X centered at 80 which is given in table 11 as the some K equals zero to infinity uh, negative one to the chaos Power Times X to the two k power all over to K factorial. And to get from the coastline of X to the coastline of X cubed we should the plug in x cubed in for the X and the power Siri&#x27;s So then this will become serious from cable zero to infinity of negative one to the K I&#x27;m x cubed raised to the two k power all over to K factorial. But we know the way we have a number with exponents raised to another exponents. This is just that number which is X raised to the two exponents. Multiply together three times UK. But three times UK is just six k. So in all of this will be X to the six K power. Now we can write up the 1st 4 terms here starting from K equals zero. You should be negative 120 with power times X to the zero power all over zero factorial plus negative one. Where this is the cake was one term forgettable into the first power times. Extra six. Power over one factorial where there should be two times one factorial. That&#x27;s two factorial plus the cake was two term, which is negative. One squared times X to the two times six, which is 12 all over two times two, which is four factorial plus the Caicos. Three term, which is negative. One cubed times acts to the six times three, which is 18th power all over two times three, which is six factorial and so on. Now we can simplify these terms a little, since everything in the first power results in a one plus negative one to the first Power is a negative one times X to the sixth over two factorial, which is just too plus negative. One squared is one times x to the 12th over four. Factorial for factorial is four times three, which is 12 times two, which is 24 plus negative. One cubed is negative. One x to the 18 over six factorial in six Factorial is six times five times four times, three times, two times once and we can break this up as six times five, which is 30 times four times three times to 30 times four is 120 times three times to 120 times three is 3 60 times two, which is 720. So this is 720 down here, and these are the 1st 4 terms.

Sara Sasani · Answer

In this video, we find the 1st 4 non zero terms off the Taylor series for the given function. The formula for the Taylor series generated by F he&#x27;s That&#x27;s some cake court zero to infinity. The case derivative off if at zero, Divided by K factorial times, takes former cake divers find, if rip off zero physical one on, then the first derivative off fr zero record to one minus for one tree on the second derivative off, a Jill is 1/4 forward re on the third. Want me? See four to minus 8/9 because all of them are No. Zero, and we only need first for non zero terms. Is there no again based on the formula. The Taylor Series for the function one minus x, divided by three over four eastern corn, too. Zero plus if crime off zero the first day of your life at zero times X plus, the secondary will give off +50 divided by two factorial transfix X squared, plus the directory. Give off with AK zero divided by three factorial friends. Excuse. After simplifying, we have the freshest for nine year terms off the Taylor series off the given function. Hope you enjoyed watching this video, and thanks for watching

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

Problem

Find the first three nonzero terms of the Taylor …

Problem 12 Easy Difficulty

Find the first three nonzero terms of the Taylor expansion for the given function and given value of a. $$\cos x \quad\left(a=\frac{\pi}{4}\right)$$

Answer

$f(x)=\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\left(x-\frac{\pi}{4}\right)-\frac{\sqrt{2}}{4}\left(x-\frac{\pi}{4}\right)^{2}+\cdots$

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$f(x)=\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\left(x-\frac{\pi}{4}\right)-\frac{\sqrt{2}}{4}\left(x-\frac{\pi}{4}\right)^{2}+\cdots$

Basic Technical Mathematics with Calculus

Grace H.

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

Grace H.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus