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CalculusCalculus10th Edition

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Chapter 10.1, Problem 82E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Solutions

Chapter
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Problem 1E
Problem 2E
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Problem 4E
Problem 5E
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Problem 7E
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Problem 10E
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Problem 17E
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Problem 21E
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Problem 23E
Problem 24E
Problem 25E
Problem 26E
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Problem 28E
Problem 29E
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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 53E
Problem 51E
Problem 52E
Problem 57E
Problem 58E
Problem 55E
Problem 54E
Problem 63E
Problem 69E
Problem 56E
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Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
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
Problem 93E
Problem 94E
Problem 95E
Problem 96E
Problem 97E
Problem 98E
BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Conjecture

Show that the equation of an ellipse can be written as

( x − h ) 2 a 2 + ( y − k ) 2 a 2 ( 1 − e 2 ) = 1 .

(b) Use a graphing utility to graph the ellipse

( x − 2 ) 2 4 + ( y − 3 ) 2 4 ( 1 − e 2 ) = 1 for e = 0.95 , e = 0.75 , e = 0.5 , e = 0.25 ,   and   e = 0

Use the results of part (b) to make a conjecture about the change in the shape of the ellipse as e approaches 0.

(a)

To determine

To prove: The equation of an ellipse can be re-written in the form of as (x−h)2a2+(y−k)2a2(1−e2)=1.

Explanation

Given:

The equation, (x−h)2a2+(y−k)2a2(1−e2)=1.

Formula used:

The standard equation of an ellipse is, (x−h)2a2+(y−k)2b2=1 and eccentricity of the ellipse formulated by the equation e=a2−b2a2.

Proof:

Consider the standard equation of the ellipse, (x−h)2a2+(y−k)2b2=1.

Since, the eccentricity of the ellipse is formulated as, e2=a2−b2a2

(b)

To determine

To graph: The ellipse, (x−2)24+(y−3)24(1−e2)=1 for different values of e with the use of graphing utility.

(c)

To determine
The conjecture of the change in shape of the graph of the ellipse in part (b) as e approaches 0.

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Divergence and Curl In Exercises 19-26, find (a) the divergence of the vector field and (b) the curl of the vec...

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In Review Exercises 14 to 17, sketch and describe the locus in space. Find the locus of points equidistant from...

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SAVINGS ACCOUNTS The Pirerras are planning to go to Europe 3 years from now and have agreed to set aside 150/mo...

Finite Mathematics for the Managerial, Life, and Social Sciences

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