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Math
CalculusMultivariable Calculus8th Edition

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Chapter 11.2, Problem 79E
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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
Problem 82E
Problem 83E
Problem 84E
Problem 85E
Problem 86E
Problem 87E
Problem 88E
Problem 89E
Problem 90E
Problem 91E
Problem 92E
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

The figure shows two circles C and D of radius 1 that touch at P. The line T is a common tangent line; C1 is the circle that touches C, D, and T; C2 is the circle that touches C, D, and C1; C3 is the circle that touches C, D, and C2. This procedure can be continued indefinitely and produces an infinite sequence of circles {Cn}. Find an expression for the diameter of Cn and thus provide another geometric demonstration of Example 8.

Chapter 11.2, Problem 79E, The figure shows two circles C and D of radius 1 that touch at P. The line T is a common tangent

To determine

To find: The expression for the diameter cn .

Explanation

Given:

The two circles C and D of radius 1 touch at P.

Calculation:

Assume that the center of the circle D is R and the center of the circle C1 is A and the triangle PRA is a right triangle

By the Pythagoras theorem,

(AP)2+(PR)2=(AR)2(1−d12)2+12=(1+d12)21−d1+d124+1=1+d1+d124

Simplify further,

1−d1+=1+d22d2=1d2=12

Assume that the center of the circle D is R and the center of the circle C2 is B and the triangle PRB is a right triangle

By the Pythagoras theorem,

(PB)2+(PR)2=(BR)2(1−(d1−d22))2+12=(1+d22)2(1−(12+d22))2+1=(1+d22)21−2(12+d22)+(12+d22)2=1+d2+d224

That is, d2=16 .

Assume that the center of the circle D is R and the center of the circle C3 is C and the triangle PRB is a right triangle

By the Pythagoras theorem

(PC)2+(PR)2=(CR)2(1−(d1+d2+d32))2+12=(1+d32)2(1−(12+16+d32))2+1=(1+d32)2(1−(23+d32))2+1=(1+d32)2

That is, d3=112 .

The diameters d1,d2 and d3 can be expressed as follows,

d1=11×2d2=12×3d3=13×4

Therefore, it can be conclude that dn=1n(n+1)

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Find the derivative of the function. y=sin(1+x2)

Calculus (MindTap Course List)

Use a stem and leaf display to organize the following distribution of scores. Use six stems with each stem corr...

Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 90-98, determine whether the statement is true or false. If it is true, explain why it is true. If...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). 8. limt2(t22t33t+5)2

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Convert the expressions in Exercises 6584 to power form. xy23

Finite Mathematics

The article Can We Really Walk Straight? (Amer. J. of Physical Anthropology, 1992: 19-27) reported on an experi...

Probability and Statistics for Engineering and the Sciences

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For Problems 2-10, state the property of equality or the property of real numbers that justifies each of the st...

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An amount of money that must be deposited today at compound interest to provide a specified lump sum of money i...

Contemporary Mathematics for Business & Consumers

36. Productivity Suppose that the rate of change of production of the average worker at a factory is given by ...

Mathematical Applications for the Management, Life, and Social Sciences

Average Student Debt The following bar graph shows the average student debt in each graduating class from 2008 ...

Mathematical Excursions (MindTap Course List)

Find each power rounded to three significant digits: 143

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In Exercise 17 to 22, use either the sine ratio or the cosine ratio to find the length of the indicated sides o...

Elementary Geometry For College Students, 7e

Find the local and absolute extreme values of the function on the given interval. f(x)=3x4x2+1,[2,2]

Single Variable Calculus: Early Transcendentals

Comparing SeriesExplain any differences among the following series. (a) n=1an (b) k=1ak (c) n=1ak

Calculus: Early Transcendental Functions (MindTap Course List)

Determining a Differentiable Function In Exercises 47 and 48, find dy / dx implicitly and find the largest inte...

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In Exercises 1- 9, let G be the given group. Write out the elements of a group of permutations that is isomorph...

Elements Of Modern Algebra

Show that 2 cis 30 and 2 cis (–30) are conjugates.

Trigonometry (MindTap Course List)

Write in cylindrical coordinates, where E is the solid at the right.

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limh04+h2h is the derivative of: a) f(x)=4+x at x = 2 b) f(x)=x at x = 4 c) f(x)=x at x = 2 d) f(x)=4+h2h at x ...

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Suppose that the base of the hexagonal pyramid in Exercise 6 has an area of 41.6cm2 and that the altitude of th...

Elementary Geometry for College Students

PRODUCTION SCHEDULING Ace Novelty manufactures Giant Pandas and Saint Bernards. Each Panda requires 1.5yd2 of p...

Finite Mathematics for the Managerial, Life, and Social Sciences

The shelf life of packaged food depends on many factors. Dry cereal is considered to be a moisture-sensitive pr...

Introduction To Statistics And Data Analysis

Using an Integrating Factor In Exercises 33-36, use theintegrating factor to find the general solution of the d...

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Modeling Data The atmospheric pressure decreases with increasing altitude. At sea level, the average air pressu...

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Finding Moments of Inertia and Radii of Gyration In Exercises 3538, find Ix,Iy,I0,x and y for the lamina bounde...

Calculus (MindTap Course List)

Explain the general advantages and disadvantages of between-subjects design compared to within-subjects design.

Research Methods for the Behavioral Sciences (MindTap Course List)

A metal bar is 758 inches long. If 932 inch is cut off one end. how long is the bar after the cut?

Mathematics For Machine Technology

Identify and explain the common threats to external validity and identify threats when they appear in a researc...

Research Methods for the Behavioral Sciences (MindTap Course List)

The Car Repair Ratings website provides consumer reviews and ratings for garages inthe United States and Canada...

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Practice Use the graph of the function f shown to determine each of the following. f-1

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A zoo has categorized its visitors into three categories: member, school, and general. The member category refe...

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