Solved: Taylor polynomials centered at a ? 0a. Find the

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Problem 28E Chapter 9.1

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 28E

Taylor polynomials centered at a ≠ 0

a. Find the nth-order Taylor polynomials for the given function centered at the given point a for n = 0, 1, and 2.

b. Graph the Taylor polynomials and the Junction.

f(x)= cos x, a = π/6

Step-by-Step Solution:

Solution 28E

Step 1:

In this problem we have to find the nth-order Taylor polynomials for cos x centered at the point  for n = 0, 1, and 2

Taylor series is given by

Let us first find order Taylor polynomial.

In our case,

That is

So, what we need to do to get desired polynomial is to calculate derivatives, evaluate them at the given point and plug results into given formula.

Then

Now use calculated values in to get the polynomial.

 

        

Thus Taylor polynomial of  upto with center  is

Step 2:

Now let us first find order Taylor polynomial.

In our case,

That is

So, what we need to do to get desired polynomial is to calculate derivatives, evaluate them at the given point and plug results into given formula.

Then

Then

Now use calculated values in  to get the polynomial.

 

        

Thus Taylor polynomial of  upto with center  is

Step 2:

Now let us first find order Taylor polynomial.

In our case,

That is

So, what we need to do to get desired polynomial is to calculate derivatives, evaluate them at the given point and plug results into given formula.

Then

Then

Then

Now use calculated values in  to get the polynomial.

 

        

Thus Taylor polynomial of  upto with center  is

Step 3:

b. Graph the Taylor polynomials and the function.

The taylor polynomial of  upto with center  is and its graph is given below

Step 4 of 6

Chapter 9.1, Problem 28E is Solved
Step 5 of 6

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 28E from 9.1 chapter was answered, more than 233 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Taylor, polynomials, given, Centered, function. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Taylor polynomials centered at a ? 0a. Find the nth-order Taylor polynomials for the given function centered at the given point a for n = 0, 1, and 2.________________b. Graph the Taylor polynomials and the Junction.f(x)= cos x, a = ?/6” is broken down into a number of easy to follow steps, and 41 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 28E from chapter: 9.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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