Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
4th Edition
ISBN: 9780133178579
Author: Ross L. Finney
Publisher: PEARSON
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Chapter 5.5, Problem 28E

a.

To determine

To determine the true change Δf=f(a+dx)−f(a)

a.

Expert Solution
Check Mark

Answer to Problem 28E

The true change is 0.231with the given values.

Explanation of Solution

Given information:

The given function is f(x)=x3−x,      a=1,   dx=0.1

The true change Δf=f(a+dx)−f(a)

  f(1)=13−1=0     [ a=1]f(1+0.1)=(1+0.1)3−(1+0.1)=0.231  [ a=1,  dx=0.1]Δf=0.231−0=0.231   [substitute the value f(1+0.1), f(1)]

Therefore,

The true change is 0.231with the given values.

b.

To determine

The estimated change df=f′(a)dx .

b.

Expert Solution
Check Mark

Answer to Problem 28E

The estimated change is 0.2 with the given values.

Explanation of Solution

Given information:

The given function is f(x)=x3−x,      a=1,   dx=0.1

The estimated change df=f′(a)dx

  f′(x)=3x2−1f′(1)=3⋅12−1=2    [a=1]df=2⋅0.1=0.2         [a=1, dx=0.1]

Therefore,

The estimated change is 0.2 with the given values.

c.

To determine

To calculate the approximation error |Δf−df|

c.

Expert Solution
Check Mark

Answer to Problem 28E

The approximation error is 3.1×10−2

Explanation of Solution

Given information:

The given function is f(x)=x3−x,      a=1,   dx=0.1

The approximation error is |Δf−df|

  Δf=0.231df=0.2|Δf−df|=|0.231−0.2|=0.031=3.1×10−2  [substitute Δf,df]

Therefore,

The approximation error is 3.1×10−2

Previous
Chapter 5.5, Problem 27E
Next
Chapter 5.5, Problem 29E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QRCh. 5.1 - Prob. 2QRCh. 5.1 - Prob. 3QRCh. 5.1 - Prob. 4QRCh. 5.1 - Prob. 5QRCh. 5.1 - Prob. 6QRCh. 5.1 - Prob. 7QRCh. 5.1 - Prob. 8QRCh. 5.1 - Prob. 9QRCh. 5.1 - Prob. 10QR
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Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Prob. 60ECh. 5.2 - Prob. 61ECh. 5.2 - Prob. 62ECh. 5.2 - Prob. 63ECh. 5.3 - Prob. 1QRCh. 5.3 - Prob. 2QRCh. 5.3 - Prob. 3QRCh. 5.3 - Prob. 4QRCh. 5.3 - Prob. 5QRCh. 5.3 - Prob. 6QRCh. 5.3 - Prob. 7QRCh. 5.3 - Prob. 8QRCh. 5.3 - Prob. 9QRCh. 5.3 - Prob. 10QRCh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - 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