/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q.10 If f聽is a function such that f(... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q.10 (page 659)

If fis a function such that f(0)=鈭�3and localid="1650438953513" role="math" f'(x)=2f(x)every value of x, find the Maclaurin series for f.

Short Answer

Expert verified

The Maclaurin series for the function f(x)is:

f(x)=-31+2x+4x22!+8x33!+鈥�

Or, it can be written as

f(x)=-3鈭�k=0x2kxkk!

Step by step solution

01

Given Information

Given equations:

f(0)=-3

f'(x)=2f(x)

02

Finding the Maclaurin series for f  

The general formula to calculate the Maclaurin series for the function is:

f(x)=f(0)+f'(0)x+f''(0)2!x2+f''(0)3!x3+鈥�

As, f(0)=-3.

f'(0)=2f(0)=2路-3=-6

So,

f''(0)=2f'(0)=2路(-6)=-12

And,

f''(0)=2f''(0)=2路-12=-24

The Maclaurin series for the function f(x)is:

f(x)=-3-6x+-12x22!+-24x33!+鈥�

=-31+2x+4x22!+8x33!+鈥�

Or, it can be written as

localid="1650438932580" f(x)=-3鈭�k=0鈭�2kxkk!

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

Most popular questions from this chapter

Find the interval of convergence for power series:鈭�k=0鈭�-1k2k+1!x2k+1

In Exercises 49鈥�56 find the Taylor series for the specified function and the given value of x0. Note: These are the same functions and values as in Exercises 41鈥�48.

52.x,1

Find the interval of convergence for power series:鈭�k=1鈭�-1kk+1xk

Prove that if x0鈭�蚁,x0+蚁is the interval of convergence for the series 鈭�k=0鈭�鈥�akx鈭�x0k, then the series converges conditionally at x0+p.

If m is a positive integer, how can we find the Maclaurin series for the function f(cxm)if we already know the Maclaurin series for the function f(x)? How do you find the interval of convergence for the new series?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.