Q 27 Use the Maclaurin series for sin... [FREE SOLUTION]

Chapter 8: Q 27 (page 704)

Use the Maclaurin series for $\sin x$ ,
$\cos x$ , and $e^{x}$ to find the values of the following series.
$1 - \frac{蟺^{2}}{2^{2} 路 2!} + \frac{蟺^{4}}{2^{4} 路 4!} - \frac{蟺^{6}}{2^{6} 路 6!} + 鈰�$

Short Answer

Expert verified

The values of the series $1 - \frac{蟺^{2}}{2^{2} 路 2!} + \frac{蟺^{4}}{2^{4} 路 4!} - \frac{蟺^{6}}{2^{6} 路 6!} + 鈰�$ is $1 - \frac{蟺^{2}}{2^{2} 路 2!} + \frac{蟺^{4}}{2^{4} 路 4!} - \frac{蟺^{6}}{2^{6} 路 6!} + 鈰� = 0$

Step by step solution

Given information

The series is $1 - \frac{蟺^{2}}{2^{2} 路 2!} + \frac{蟺^{4}}{2^{4} 路 4!} - \frac{蟺^{6}}{2^{6} 路 6!} + 鈰�$

Find the Maclaurin series for the function f(x)=sinx

The Maclaurin series for the function $f (x) = \sin x$ is

$\cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{3}}{3!} - \frac{x^{4}}{4!} + 鈰�$

The series $1 - \frac{蟺^{2}}{2^{2} 路 2!} + \frac{蟺^{4}}{2^{4} 路 4!} - \frac{蟺^{6}}{2^{6} 路 6!} + 鈰�$ is the Maclaurin series for

$\cos x$ at $x = \frac{蟺}{2}$

Find the values of the series

$1 - \frac{x^{2}}{2!} + \frac{x^{3}}{3!} - \frac{x^{4}}{4!} + 鈰� = \cos x$

Therefore,

$1 - \frac{蟺^{2}}{2^{2} 路 2!} + \frac{蟺^{4}}{2^{4} 路 4!} - \frac{蟺^{6}}{2^{6} 路 6!} + 鈰� = \cos \frac{蟺}{2} 1 - \frac{蟺^{2}}{2^{2} 路 2!} + \frac{蟺^{4}}{2^{4} 路 4!} - \frac{蟺^{6}}{2^{6} 路 6!} + 鈰� = 0$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Use the Maclaurin series for $\sin x$ ,
$\cos x$ , and $e^{x}$ to find the values of the following series.
$1 - \frac{蟺^{2}}{2^{2} 路 2!} + \frac{蟺^{4}}{2^{4} 路 4!} - \frac{蟺^{6}}{2^{6} 路 6!} + 鈰�$

Short Answer

Step by step solution

Given information

Find the Maclaurin series for the function f(x)=sinx

Find the values of the series

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Decision Maths

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

91影视

Use the Maclaurin series for sinx,cosx, and exto find the values of the following series.1-蟺222路2!+蟺424路4!-蟺626路6!+鈰�

Short Answer

Step by step solution

Given information

Find the Maclaurin series for the function f(x)=sinx

Find the values of the series

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Decision Maths

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use the Maclaurin series for $\sin x$ ,
$\cos x$ , and $e^{x}$ to find the values of the following series.
$1 - \frac{蟺^{2}}{2^{2} 路 2!} + \frac{蟺^{4}}{2^{4} 路 4!} - \frac{蟺^{6}}{2^{6} 路 6!} + 鈰�$