Explanation Given information: The area of the circle of radius r is A = π r 2 . Formula used: d d x ( x n ) = n x n − 1 Calculation: A = π r 2 (Given) Differentiating A with respect to ‘r’, we get d A d r = d d r ( π r 2 ) = π d d r ( To determine (b) To state: The representation of d A d r geometrically. To determine (c) To explain: The observations made in d A d r = 2 π r using the difference quotient.

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

See similar textbooks

Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Videos

Question

Chapter 3.1, Problem 69P

To determine

(a)

To find:

dAdr

To determine

(b)

To state:

The representation of dAdr geometrically.

To determine

(c)

To explain:

The observations made in dAdr=2πr using the difference quotient.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.1, Problem 68P

Chapter 3.1, Problem 70P

Chapter 3 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

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

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

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.

(a) To find: d A d r

Solution Summary: The author states that the area of the circle of radius r is A=pi r2.

Concept explainers

Videos

(a)

To find:

dAdr

(b)

To state:

The representation of dAdr geometrically.

(c)

To explain:

The observations made in dAdr=2πr using the difference quotient.

Want to see the full answer?

Chapter 3 Solutions

(a) To find: d A d r

Solution Summary: The author states that the area of the circle of radius r is A=pi r2.

Concept explainers

Videos

(a) To find: dAdr

(b) To state: The representation of dAdr geometrically.

(c) To explain: The observations made in dAdr=2πr using the difference quotient.

Want to see the full answer?

Chapter 3 Solutions

(a)

To find:

dAdr

(b)

To state:

The representation of dAdr geometrically.

(c)

To explain:

The observations made in dAdr=2πr using the difference quotient.