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Math Calculus EBK CALCULUS: EARLY TRANSCENDENTALS

That r = f 1 ( θ ) and r = f 2 ( θ ) define the same curves in polar coordinates if f 1 ( θ ) = − f 2 ( θ + π ) and use this to show that the following define the same conic section : r = d e 1 − e cos θ , r = − d e 1 + e cos θ

That r = f 1 ( θ ) and r = f 2 ( θ ) define the same curves in polar coordinates if f 1 ( θ ) = − f 2 ( θ + π ) and use this to show that the following define the same conic section : r = d e 1 − e cos θ , r = − d e 1 + e cos θ

EBK CALCULUS: EARLY TRANSCENDENTALS

EBK CALCULUS: EARLY TRANSCENDENTALS

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Question

Chapter 11, Problem 40CRE

To determine

That $r = f_{1} (θ)$ and $r = f_{2} (θ)$ define the same curves in polar coordinates if $f_{1} (θ) = - f_{2} (θ + π)$ and use this to show that the following define the same conic section: $r = \frac{d e}{1 - e \cos θ}, r = \frac{- d e}{1 + e \cos θ}$

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Chapter 11, Problem 39CRE

Chapter 11, Problem 41CRE

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Chapter 11 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 6PQ Ch. 11.1 - Prob. 7PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E

Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Prob. 40E Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.1 - Prob. 47E Ch. 11.1 - Prob. 48E Ch. 11.1 - Prob. 49E Ch. 11.1 - Prob. 50E Ch. 11.1 - Prob. 51E Ch. 11.1 - Prob. 52E Ch. 11.1 - Prob. 53E Ch. 11.1 - Prob. 54E Ch. 11.1 - Prob. 55E Ch. 11.1 - Prob. 56E Ch. 11.1 - Prob. 57E Ch. 11.1 - Prob. 58E Ch. 11.1 - Prob. 59E Ch. 11.1 - Prob. 60E Ch. 11.1 - Prob. 61E Ch. 11.1 - Prob. 62E Ch. 11.1 - Prob. 63E Ch. 11.1 - Prob. 64E Ch. 11.1 - Prob. 65E Ch. 11.1 - Prob. 66E Ch. 11.1 - Prob. 67E Ch. 11.1 - Prob. 68E Ch. 11.1 - Prob. 69E Ch. 11.1 - Prob. 70E Ch. 11.1 - Prob. 71E Ch. 11.1 - Prob. 72E Ch. 11.1 - Prob. 73E Ch. 11.1 - Prob. 74E Ch. 11.1 - Prob. 75E Ch. 11.1 - Prob. 76E Ch. 11.1 - Prob. 77E Ch. 11.1 - Prob. 78E Ch. 11.1 - Prob. 79E Ch. 11.1 - Prob. 80E Ch. 11.1 - Prob. 81E Ch. 11.1 - Prob. 82E Ch. 11.1 - Prob. 83E Ch. 11.1 - Prob. 84E Ch. 11.1 - Prob. 85E Ch. 11.1 - Prob. 86E Ch. 11.1 - Prob. 87E Ch. 11.1 - Prob. 88E Ch. 11.1 - Prob. 89E Ch. 11.1 - Prob. 90E Ch. 11.1 - Prob. 91E Ch. 11.1 - Prob. 92E Ch. 11.1 - Prob. 93E Ch. 11.1 - Prob. 94E Ch. 11.1 - Prob. 95E Ch. 11.1 - Prob. 96E Ch. 11.1 - Prob. 97E Ch. 11.1 - Prob. 98E Ch. 11.1 - Prob. 99E Ch. 11.1 - Prob. 100E Ch. 11.1 - Prob. 101E Ch. 11.1 - Prob. 102E Ch. 11.1 - Prob. 103E Ch. 11.1 - Prob. 104E Ch. 11.1 - Prob. 105E Ch. 11.1 - Prob. 106E Ch. 11.1 - Prob. 107E Ch. 11.1 - Prob. 108E Ch. 11.1 - Prob. 109E Ch. 11.2 - Prob. 1PQ Ch. 11.2 - Prob. 2PQ Ch. 11.2 - Prob. 3PQ Ch. 11.2 - Prob. 4PQ Ch. 11.2 - Prob. 5PQ Ch. 11.2 - Prob. 6PQ Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Prob. 33E Ch. 11.2 - Prob. 34E Ch. 11.2 - Prob. 35E Ch. 11.2 - Prob. 36E Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.3 - Prob. 1PQ Ch. 11.3 - Prob. 2PQ Ch. 11.3 - Prob. 3PQ Ch. 11.3 - Prob. 4PQ Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E Ch. 11.3 - Prob. 10E Ch. 11.3 - Prob. 11E Ch. 11.3 - Prob. 12E Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - Prob. 16E Ch. 11.3 - Prob. 17E Ch. 11.3 - Prob. 18E Ch. 11.3 - Prob. 19E Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Prob. 29E Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Prob. 33E Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Prob. 37E Ch. 11.3 - Prob. 38E Ch. 11.3 - Prob. 39E Ch. 11.3 - Prob. 40E Ch. 11.3 - Prob. 41E Ch. 11.3 - Prob. 42E Ch. 11.3 - Prob. 43E Ch. 11.3 - Prob. 44E Ch. 11.3 - Prob. 45E Ch. 11.3 - Prob. 46E Ch. 11.3 - Prob. 47E Ch. 11.3 - Prob. 48E Ch. 11.3 - Prob. 49E Ch. 11.3 - Prob. 50E Ch. 11.3 - Prob. 51E Ch. 11.3 - Prob. 52E Ch. 11.3 - Prob. 53E Ch. 11.3 - Prob. 54E Ch. 11.3 - Prob. 55E Ch. 11.3 - Prob. 56E Ch. 11.3 - Prob. 57E Ch. 11.3 - Prob. 58E Ch. 11.3 - Prob. 59E Ch. 11.3 - Prob. 60E Ch. 11.3 - Prob. 61E Ch. 11.3 - Prob. 62E Ch. 11.3 - Prob. 63E Ch. 11.3 - Prob. 64E Ch. 11.4 - Prob. 1PQ Ch. 11.4 - Prob. 2PQ Ch. 11.4 - Prob. 3PQ Ch. 11.4 - Prob. 1E Ch. 11.4 - Prob. 2E Ch. 11.4 - Prob. 3E Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Prob. 21E Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - Prob. 25E Ch. 11.4 - Prob. 26E Ch. 11.4 - Prob. 27E Ch. 11.4 - Prob. 28E Ch. 11.4 - Prob. 29E Ch. 11.4 - Prob. 30E Ch. 11.4 - Prob. 31E Ch. 11.4 - Prob. 32E Ch. 11.4 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.4 - Prob. 35E Ch. 11.4 - Prob. 36E Ch. 11.4 - Prob. 37E Ch. 11.4 - Prob. 38E Ch. 11.4 - Prob. 39E Ch. 11.4 - Prob. 40E Ch. 11.4 - Prob. 41E Ch. 11.4 - Prob. 42E Ch. 11.4 - Prob. 43E Ch. 11.4 - Prob. 44E Ch. 11.5 - Prob. 1PQ Ch. 11.5 - Prob. 2PQ Ch. 11.5 - Prob. 3PQ Ch. 11.5 - Prob. 4PQ Ch. 11.5 - Prob. 1E Ch. 11.5 - Prob. 2E Ch. 11.5 - Prob. 3E Ch. 11.5 - Prob. 4E Ch. 11.5 - Prob. 5E Ch. 11.5 - Prob. 6E Ch. 11.5 - Prob. 7E Ch. 11.5 - Prob. 8E Ch. 11.5 - Prob. 9E Ch. 11.5 - Prob. 10E Ch. 11.5 - Prob. 11E Ch. 11.5 - Prob. 12E Ch. 11.5 - Prob. 13E Ch. 11.5 - Prob. 14E Ch. 11.5 - Prob. 15E Ch. 11.5 - Prob. 16E Ch. 11.5 - Prob. 17E Ch. 11.5 - Prob. 18E Ch. 11.5 - Prob. 19E Ch. 11.5 - Prob. 20E Ch. 11.5 - Prob. 21E Ch. 11.5 - Prob. 22E Ch. 11.5 - Prob. 23E Ch. 11.5 - Prob. 24E Ch. 11.5 - Prob. 25E Ch. 11.5 - Prob. 26E Ch. 11.5 - Prob. 27E Ch. 11.5 - Prob. 28E Ch. 11.5 - Prob. 29E Ch. 11.5 - Prob. 30E Ch. 11.5 - Prob. 31E Ch. 11.5 - Prob. 32E Ch. 11.5 - Prob. 33E Ch. 11.5 - Prob. 34E Ch. 11.5 - Prob. 35E Ch. 11.5 - Prob. 36E Ch. 11.5 - Prob. 37E Ch. 11.5 - Prob. 38E Ch. 11.5 - Prob. 39E Ch. 11.5 - Prob. 40E Ch. 11.5 - Prob. 41E Ch. 11.5 - Prob. 42E Ch. 11.5 - Prob. 43E Ch. 11.5 - Prob. 44E Ch. 11.5 - Prob. 45E Ch. 11.5 - Prob. 46E Ch. 11.5 - Prob. 47E Ch. 11.5 - Prob. 48E Ch. 11.5 - Prob. 49E Ch. 11.5 - Prob. 50E Ch. 11.5 - Prob. 51E Ch. 11.5 - Prob. 52E Ch. 11.5 - Prob. 53E Ch. 11.5 - Prob. 54E Ch. 11.5 - Prob. 55E Ch. 11.5 - Prob. 56E Ch. 11.5 - Prob. 57E Ch. 11.5 - Prob. 58E Ch. 11.5 - Prob. 59E Ch. 11.5 - Prob. 60E Ch. 11.5 - Prob. 61E Ch. 11.5 - Prob. 62E Ch. 11.5 - Prob. 63E Ch. 11.5 - Prob. 64E Ch. 11.5 - Prob. 65E Ch. 11.5 - Prob. 66E Ch. 11.5 - Prob. 67E Ch. 11.5 - Prob. 68E Ch. 11.5 - Prob. 69E Ch. 11.5 - Prob. 70E Ch. 11.5 - Prob. 71E Ch. 11.5 - Prob. 72E Ch. 11.5 - Prob. 73E Ch. 11.5 - Prob. 74E Ch. 11.5 - Prob. 75E Ch. 11.5 - Prob. 76E Ch. 11.5 - Prob. 77E Ch. 11.5 - Prob. 78E Ch. 11 - Prob. 1CRE Ch. 11 - Prob. 2CRE Ch. 11 - Prob. 3CRE Ch. 11 - Prob. 4CRE Ch. 11 - Prob. 5CRE Ch. 11 - Prob. 6CRE Ch. 11 - Prob. 7CRE Ch. 11 - Prob. 8CRE Ch. 11 - Prob. 9CRE Ch. 11 - Prob. 10CRE Ch. 11 - Prob. 11CRE Ch. 11 - Prob. 12CRE Ch. 11 - Prob. 13CRE Ch. 11 - Prob. 14CRE Ch. 11 - Prob. 15CRE Ch. 11 - Prob. 16CRE Ch. 11 - Prob. 17CRE Ch. 11 - Prob. 18CRE Ch. 11 - Prob. 19CRE Ch. 11 - Prob. 20CRE Ch. 11 - Prob. 21CRE Ch. 11 - Prob. 22CRE Ch. 11 - Prob. 23CRE Ch. 11 - Prob. 24CRE Ch. 11 - Prob. 25CRE Ch. 11 - Prob. 26CRE Ch. 11 - Prob. 27CRE Ch. 11 - Prob. 28CRE Ch. 11 - Prob. 29CRE Ch. 11 - Prob. 30CRE Ch. 11 - Prob. 31CRE Ch. 11 - Prob. 32CRE Ch. 11 - Prob. 33CRE Ch. 11 - Prob. 34CRE Ch. 11 - Prob. 35CRE Ch. 11 - Prob. 36CRE Ch. 11 - Prob. 37CRE Ch. 11 - Prob. 38CRE Ch. 11 - Prob. 39CRE Ch. 11 - Prob. 40CRE Ch. 11 - Prob. 41CRE Ch. 11 - Prob. 42CRE Ch. 11 - Prob. 43CRE Ch. 11 - Prob. 44CRE Ch. 11 - Prob. 45CRE Ch. 11 - Prob. 46CRE Ch. 11 - Prob. 47CRE Ch. 11 - Prob. 48CRE Ch. 11 - Prob. 49CRE Ch. 11 - Prob. 50CRE Ch. 11 - Prob. 51CRE Ch. 11 - Prob. 52CRE Ch. 11 - Prob. 53CRE Ch. 11 - Prob. 54CRE Ch. 11 - Prob. 55CRE

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