/*! 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. 2 In each problem that follows we ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 2 (page 569)

In each problem that follows we are given values for f(c)and f'(c)for some cUse this information to approximate f(c+h)for the given value of h.

a)f(0)=2,f'(0)=1,h=1

b)f(1)=-1,f'(1)=-3,h=0.5

c)f(-2)=-3,f'(-2)=2,h=0.25

d)f(1.5)=6.2,f'(1.5)=2.2,h=0.1

Short Answer

Expert verified

The linear approximation are:

a)f(1)=3

b)f(1.5)=-2.5

c)f(-1.75)=-2.5

d)f(1.6)=6.42

Step by step solution

01

Step 1. Given information

a)f(0)=2,f'(0)=1,h=1

b)f(1)=鈭�1,f'(1)=鈭�3,h=0.5

c)f(鈭�2)=鈭�3,f'(鈭�2)=2,h=0.25

d)f(1.5)=6.2,f'(1.5)=2.2,h=0.1

02

Part(a) step 1. Evaluate linear approximation.

The linear approximation is given by a formula:f(c+h)=f(c)+hf'(c)

Givenf(0+1)=f(0)+1.f'(0)f(1)=2+1(1)f(1)=3

03

Part (b) step 1. Evaluate linear approximation.

f(c+h)=f(c)+hf'(c)f(1+0.5)=f(1)+(0.5)f'(1)f(1.5)=-1+(0.5)(-3)f(1.5)=-1-1.5f(1.5)=-2.5

04

Part(c) step 1. Evaluate linear approximation.

f(c+h)=f(c)+hf'(c)f(-2+0.25)=f(-2)+(0.25)f'(-2)f(-1.75)=-3+(0.25)(2)f(-1.75)=-3+0.5f(-1.75)=-2.5

05

Part(d) step 1. Evaluate linear approximation.

f(c+h)=f(c)+hf'(c)f(1.5+0.1)=f(1.5)+(0.1)f'(1.5)f(1.6)=6.2+(0.1)(2.2)f(1.6)=6.2+0.22f(1.6)=6.42

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

Consider the region between the graph of fx=x-2and the x-axis on [2, 5]. For each line of rotation given in Exercises 35鈥�40, use definite integrals to find the volume of the resulting solid.

Find the exact value of the arc length of each function f (x) on [a, b] by writing the arc length as a definite integral and then solving that integral.

fx=4-x ,a,b=2,5

Sketching disks ,washers and shells : sketch the three disks , washers , shells that result from revolving the rectangles shown in the figure around the given lines

y axis .

Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.

dydx=2xy

Each of the definite integrals in Exercises 19鈥�24 represents the volume of a solid of revolution obtained by rotating a region around either the x- or y-axis. Find this region.
蟺鈭�1316-x+12dx
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Logic and Functions

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.