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

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 3.3, Problem 59E

(a)

To determine

The meaning of rejected quantity.

(a)

Expert Solution

Answer to Problem 59E

The amount dx will get rejected.

Explanation of Solution

Given information:

The given statement:

“It is useful to consider quantities infinity small such that when their ratio is sought, they may not be consider zero, but which are rejected as often as they occur with quantities incomparably greater. Thus, if we have x+dx , dx is rejected. Similarly, we cannot have xdx and dxdx standing together, as xdx is incomparably greater than dxdx.

Hence, if we are to differentiate uv , we write

d(uv)=(u+du)(v+dv)−uv=uv+vdu+udv+dudv−uv=vdu+udv ”

In the given statement the word “rejected” mean

“The small amount like a constant over infinity is so small it did not change anything and thus should be ignored to facilitate the problem."

Let x+dx be a total quantity where dx is a small fraction.

Hence, the amount dx will get rejected.

(b)

To determine

The status of the quantity dudv.

(b)

Expert Solution

Answer to Problem 59E

The amount dudv will get rejected.

Explanation of Solution

Given information:

The given statement:

“It is useful to consider quantities infinity small such that when their ratio is sought, they may not be consider zero, but which are rejected as often as they occur with quantities incomparably greater. Thus if we have x+dx , dx is rejected. Similarly we cannot have xdx and dxdx standing together, as xdx is incomparably greater than dxdx . Hence if we are to differentiate uv , we write

d(uv)=(u+du)(v+dv)−uv=uv+vdu+udv+dudv−uv=vdu+udv ”

The given quantity is dudv.

Since, dudv is incomparably smaller than the term vdu,udv.

Hence, the amount dudv will get rejected.

(c)

To determine

To calculate: The value of the function.

(c)

Expert Solution

Answer to Problem 59E

The expression results formula of product rule of the differentiation.

Explanation of Solution

Given information:

The given function is d(uv)=vdu+udv.

Calculation:

The function is d(uv)=vdu+udv.

Divide the above function each with respect to dx.

ddx(uv)=vdudx+udvdx

Hence, the expression results formula of product rule of the differentiation.

(d)

To determine

Critics of Leibniz 's time objected to dividing the equation by dx both sides dx.

(d)

Expert Solution

Answer to Problem 59E

The critics is “dividing by dx is similar to the division by 0”.

Explanation of Solution

Given information:

The given function is d(uv)=vdu+udv.

The quantity is dx.

Since, dx is incomparably small.

Hence, the critics is “dividing by dx is similar to the division by 0”.

(e)

To determine

Critics of Leibniz 's time objected to dividing the equation by dx both sides dx.

(e)

Expert Solution

Answer to Problem 59E

The Leibniz’s division rule is d(uv)=vdu−udvv2.

Explanation of Solution

Given information:

The given functions are u,v.

Calculation:

The function are u,v.

d(uv)=u+duv+dv−uv=(u+du)v−u(v+dv)(v+dv)v=uv+vdu−uv−udvv2+vdv=vdu−udvv2

Hence, the Leibniz’s division rule is d(uv)=vdu−udvv2.

Chapter 3.3, Problem 58E

Chapter 3.3, Problem 1QQ

Chapter 3 Solutions

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

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.2 - Prob. 1QR Ch. 3.2 - Prob. 2QR Ch. 3.2 - Prob. 3QR Ch. 3.2 - Prob. 4QR Ch. 3.2 - Prob. 5QR Ch. 3.2 - Prob. 6QR Ch. 3.2 - Prob. 7QR Ch. 3.2 - Prob. 8QR Ch. 3.2 - Prob. 9QR Ch. 3.2 - Prob. 10QR Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - Prob. 10E Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.2 - Prob. 18E Ch. 3.2 - Prob. 19E Ch. 3.2 - Prob. 20E Ch. 3.2 - Prob. 21E Ch. 3.2 - Prob. 22E Ch. 3.2 - Prob. 23E Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - Prob. 26E Ch. 3.2 - Prob. 27E Ch. 3.2 - Prob. 28E Ch. 3.2 - Prob. 29E Ch. 3.2 - Prob. 30E Ch. 3.2 - Prob. 31E Ch. 3.2 - Prob. 32E Ch. 3.2 - Prob. 33E Ch. 3.2 - Prob. 34E Ch. 3.2 - Prob. 35E Ch. 3.2 - Prob. 36E Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Prob. 41E Ch. 3.2 - Prob. 42E Ch. 3.2 - Prob. 43E Ch. 3.2 - Prob. 44E Ch. 3.2 - Prob. 45E Ch. 3.2 - Prob. 46E Ch. 3.2 - Prob. 47E Ch. 3.2 - Prob. 48E Ch. 3.3 - Prob. 1QR Ch. 3.3 - Prob. 2QR Ch. 3.3 - Prob. 3QR Ch. 3.3 - Prob. 4QR Ch. 3.3 - Prob. 5QR Ch. 3.3 - Prob. 6QR Ch. 3.3 - Prob. 7QR Ch. 3.3 - Prob. 8QR Ch. 3.3 - Prob. 9QR Ch. 3.3 - Prob. 10QR Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Prob. 10E Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Prob. 14E Ch. 3.3 - Prob. 15E Ch. 3.3 - Prob. 16E Ch. 3.3 - Prob. 17E Ch. 3.3 - Prob. 18E Ch. 3.3 - Prob. 19E Ch. 3.3 - Prob. 20E Ch. 3.3 - Prob. 21E Ch. 3.3 - Prob. 22E Ch. 3.3 - Prob. 23E Ch. 3.3 - Prob. 24E Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3.3 - Prob. 27E Ch. 3.3 - Prob. 28E Ch. 3.3 - Prob. 29E Ch. 3.3 - Prob. 30E Ch. 3.3 - Prob. 31E Ch. 3.3 - Prob. 32E Ch. 3.3 - Prob. 33E Ch. 3.3 - Prob. 34E Ch. 3.3 - Prob. 35E Ch. 3.3 - Prob. 36E Ch. 3.3 - Prob. 37E Ch. 3.3 - Prob. 38E Ch. 3.3 - Prob. 39E Ch. 3.3 - Prob. 40E Ch. 3.3 - Prob. 41E Ch. 3.3 - Prob. 42E Ch. 3.3 - Prob. 43E Ch. 3.3 - Prob. 44E Ch. 3.3 - Prob. 45E Ch. 3.3 - Prob. 46E Ch. 3.3 - Prob. 47E Ch. 3.3 - Prob. 48E Ch. 3.3 - Prob. 49E Ch. 3.3 - Prob. 50E Ch. 3.3 - Prob. 51E Ch. 3.3 - Prob. 52E Ch. 3.3 - Prob. 53E Ch. 3.3 - Prob. 54E Ch. 3.3 - Prob. 55E Ch. 3.3 - Prob. 56E Ch. 3.3 - Prob. 57E Ch. 3.3 - Prob. 58E Ch. 3.3 - Prob. 59E Ch. 3.3 - Prob. 1QQ Ch. 3.3 - Prob. 2QQ Ch. 3.3 - Prob. 3QQ Ch. 3.3 - Prob. 4QQ Ch. 3.4 - Prob. 1QR Ch. 3.4 - Prob. 2QR Ch. 3.4 - Prob. 3QR Ch. 3.4 - Prob. 4QR Ch. 3.4 - Prob. 5QR Ch. 3.4 - Prob. 6QR Ch. 3.4 - Prob. 7QR Ch. 3.4 - Prob. 8QR Ch. 3.4 - Prob. 9QR Ch. 3.4 - Prob. 10QR Ch. 3.4 - Prob. 1E Ch. 3.4 - Prob. 2E Ch. 3.4 - Prob. 3E Ch. 3.4 - Prob. 4E Ch. 3.4 - Prob. 5E Ch. 3.4 - Prob. 6E Ch. 3.4 - Prob. 7E Ch. 3.4 - Prob. 8E Ch. 3.4 - Prob. 9E Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Prob. 12E Ch. 3.4 - Prob. 13E Ch. 3.4 - Prob. 14E Ch. 3.4 - Prob. 15E Ch. 3.4 - Prob. 16E Ch. 3.4 - Prob. 17E Ch. 3.4 - Prob. 18E Ch. 3.4 - Prob. 19E Ch. 3.4 - Prob. 20E Ch. 3.4 - Prob. 21E Ch. 3.4 - Prob. 22E Ch. 3.4 - Prob. 23E Ch. 3.4 - Prob. 24E Ch. 3.4 - Prob. 25E Ch. 3.4 - Prob. 26E Ch. 3.4 - Prob. 27E Ch. 3.4 - Prob. 28E Ch. 3.4 - Prob. 29E Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Prob. 35E Ch. 3.4 - Prob. 36E Ch. 3.4 - Prob. 37E Ch. 3.4 - Prob. 38E Ch. 3.4 - Prob. 39E Ch. 3.4 - Prob. 40E Ch. 3.4 - Prob. 41E Ch. 3.4 - Prob. 42E Ch. 3.4 - Prob. 43E Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Prob. 47E Ch. 3.4 - Prob. 48E Ch. 3.4 - Prob. 49E Ch. 3.4 - Prob. 50E Ch. 3.5 - Prob. 1QR Ch. 3.5 - Prob. 2QR Ch. 3.5 - Prob. 3QR Ch. 3.5 - Prob. 4QR Ch. 3.5 - Prob. 5QR Ch. 3.5 - Prob. 6QR Ch. 3.5 - Prob. 7QR Ch. 3.5 - Prob. 8QR Ch. 3.5 - Prob. 9QR Ch. 3.5 - Prob. 10QR Ch. 3.5 - Prob. 1E Ch. 3.5 - Prob. 2E Ch. 3.5 - Prob. 3E Ch. 3.5 - Prob. 4E Ch. 3.5 - Prob. 5E Ch. 3.5 - Prob. 6E Ch. 3.5 - Prob. 7E Ch. 3.5 - Prob. 8E Ch. 3.5 - Prob. 9E Ch. 3.5 - Prob. 10E Ch. 3.5 - Prob. 11E Ch. 3.5 - Prob. 12E Ch. 3.5 - Prob. 13E Ch. 3.5 - Prob. 14E Ch. 3.5 - Prob. 15E Ch. 3.5 - Prob. 16E Ch. 3.5 - Prob. 17E Ch. 3.5 - Prob. 18E Ch. 3.5 - Prob. 19E Ch. 3.5 - Prob. 20E Ch. 3.5 - Prob. 21E Ch. 3.5 - Prob. 22E Ch. 3.5 - Prob. 23E Ch. 3.5 - Prob. 24E Ch. 3.5 - Prob. 25E Ch. 3.5 - Prob. 26E Ch. 3.5 - Prob. 27E Ch. 3.5 - Prob. 28E Ch. 3.5 - Prob. 29E Ch. 3.5 - Prob. 30E Ch. 3.5 - Prob. 31E Ch. 3.5 - Prob. 32E Ch. 3.5 - Prob. 33E Ch. 3.5 - Prob. 34E Ch. 3.5 - Prob. 35E Ch. 3.5 - Prob. 36E Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - Prob. 40E Ch. 3.5 - Prob. 41E Ch. 3.5 - Prob. 42E Ch. 3.5 - Prob. 43E Ch. 3.5 - Prob. 44E Ch. 3.5 - Prob. 45E Ch. 3.5 - Prob. 46E Ch. 3.5 - Prob. 47E Ch. 3.5 - Prob. 48E Ch. 3.5 - Prob. 49E Ch. 3.5 - Prob. 50E Ch. 3.5 - Prob. 51E Ch. 3.5 - Prob. 52E Ch. 3.5 - Prob. 1QQ Ch. 3.5 - Prob. 2QQ Ch. 3.5 - Prob. 3QQ Ch. 3.5 - Prob. 4QQ Ch. 3 - Prob. 1RE Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Prob. 26RE Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE Ch. 3 - Prob. 74RE Ch. 3 - Prob. 75RE Ch. 3 - Prob. 76RE Ch. 3 - Prob. 77RE Ch. 3 - Prob. 78RE Ch. 3 - Prob. 79RE Ch. 3 - Prob. 80RE Ch. 3 - Prob. 81RE Ch. 3 - Prob. 82RE Ch. 3 - Prob. 83RE

Additional Math Textbook Solutions

Find more solutions based on key concepts

Repeated linear factors Evaluate the following integrals. 27. 81x39x2dx

Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

The exact value of the expression 2sin−22.5°cos−22.5° .

Precalculus

In Problems 31-42: (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d...

Precalculus (10th Edition)

Find the slopes of the following lines. The line going through the points (2,5)and(2,8).

Calculus & Its Applications (14th Edition)

The intercepts of the equation 9 x 2 +4y=36 are ______. (pp.18-19)

Precalculus Enhanced with Graphing Utilities (7th Edition)

Evaluate the integrals in Exercises 17–66. 41.

University Calculus: Early Transcendentals (4th Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning

Calculus: Early Transcendentals

Calculus

ISBN:9781285741550

Author:James Stewart

Publisher:Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:9780134438986

Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:9780134763644

Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:9781319050740

Author:Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:W. H. Freeman

Precalculus

Calculus

ISBN:9780135189405

Author:Michael Sullivan

Publisher:PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:9781337552516

Author:Ron Larson, Bruce H. Edwards

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

Evaluating Indefinite Integrals; Author: Professor Dave Explains;https://www.youtube.com/watch?v=-xHA2RjVkwY;License: Standard YouTube License, CC-BY

Calculus - Lesson 16 | Indefinite and Definite Integrals | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=bMnMzNKL9Ks;License: Standard YouTube License, CC-BY