Explanation Given: The given function is y = e θ sec θ . Calculation: Given: the given point is θ = π 4 . The equation for the slope of the tangent line to y = e θ sec θ is d y d θ . y = e θ sec θ d y d θ = d d θ e θ ⋅ sec θ + d d θ ( sec θ ) ⋅ e θ ⇒ d y d t = e θ sec θ + ( sec θ tan θ ) e θ Therefore, at θ = π 4 slope of the tangent line is d y d θ | θ = π 4 . d y d θ | θ = π 4 = e θ sec θ + ( sec θ tan θ ) e θ = e π 4 ( sec θ + sec θ tan θ ) = e π 4 ( sec π 4 + sec π 4 tan π 4 ) = e π 4 ( 2 + 2 ⋅ 1 ) = 2

4th Edition

ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 3.6, Problem 34E

To determine

To find: the equation of the tangent line at the indicated point θ=π4.

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Chapter 3.6, Problem 33E

Chapter 3.6, Problem 35E

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Chapter 3 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

Ch. 3.1 - Prob. 1PQ Ch. 3.1 - Prob. 2PQ Ch. 3.1 - Prob. 3PQ Ch. 3.1 - Prob. 4PQ Ch. 3.1 - Prob. 5PQ Ch. 3.1 - Prob. 6PQ Ch. 3.1 - Prob. 7PQ 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. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - 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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. 53E Ch. 3.5 - Prob. 54E Ch. 3.6 - Prob. 1PQ Ch. 3.6 - Prob. 2PQ Ch. 3.6 - Prob. 3PQ Ch. 3.6 - Prob. 4PQ Ch. 3.6 - Prob. 1E Ch. 3.6 - Prob. 2E Ch. 3.6 - Prob. 3E Ch. 3.6 - Prob. 4E Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - Prob. 8E Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Prob. 11E Ch. 3.6 - Prob. 12E Ch. 3.6 - Prob. 13E Ch. 3.6 - Prob. 14E Ch. 3.6 - Prob. 15E Ch. 3.6 - Prob. 16E Ch. 3.6 - Prob. 17E Ch. 3.6 - Prob. 18E Ch. 3.6 - Prob. 19E Ch. 3.6 - Prob. 20E Ch. 3.6 - Prob. 21E Ch. 3.6 - Prob. 22E Ch. 3.6 - Prob. 23E Ch. 3.6 - Prob. 24E Ch. 3.6 - 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Prob. 93E Ch. 3.9 - Prob. 1PQ Ch. 3.9 - Prob. 2PQ Ch. 3.9 - Prob. 3PQ Ch. 3.9 - Prob. 4PQ Ch. 3.9 - Prob. 5PQ Ch. 3.9 - Prob. 1E Ch. 3.9 - Prob. 2E Ch. 3.9 - Prob. 3E Ch. 3.9 - Prob. 4E Ch. 3.9 - Prob. 5E Ch. 3.9 - Prob. 6E Ch. 3.9 - Prob. 7E Ch. 3.9 - Prob. 8E Ch. 3.9 - Prob. 9E Ch. 3.9 - Prob. 10E Ch. 3.9 - Prob. 11E Ch. 3.9 - Prob. 12E Ch. 3.9 - Prob. 13E Ch. 3.9 - Prob. 14E Ch. 3.9 - Prob. 15E Ch. 3.9 - Prob. 16E Ch. 3.9 - Prob. 17E Ch. 3.9 - Prob. 18E Ch. 3.9 - Prob. 19E Ch. 3.9 - Prob. 20E Ch. 3.9 - Prob. 21E Ch. 3.9 - Prob. 22E Ch. 3.9 - Prob. 23E Ch. 3.9 - Prob. 24E Ch. 3.9 - Prob. 25E Ch. 3.9 - Prob. 26E Ch. 3.9 - Prob. 27E Ch. 3.9 - Prob. 28E Ch. 3.9 - Prob. 29E Ch. 3.9 - Prob. 30E Ch. 3.9 - Prob. 31E Ch. 3.9 - Prob. 32E Ch. 3.9 - Prob. 33E Ch. 3.9 - Prob. 34E Ch. 3.9 - Prob. 35E Ch. 3.9 - Prob. 36E Ch. 3.9 - Prob. 37E Ch. 3.9 - Prob. 38E Ch. 3.9 - Prob. 39E Ch. 3.9 - Prob. 40E Ch. 3.9 - Prob. 41E Ch. 3.9 - Prob. 42E Ch. 3.9 - Prob. 43E Ch. 3.9 - Prob. 44E Ch. 3.9 - Prob. 45E Ch. 3.9 - 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Prob. 2E Ch. 3.10 - Prob. 3E Ch. 3.10 - Prob. 4E Ch. 3.10 - Prob. 5E Ch. 3.10 - Prob. 6E Ch. 3.10 - Prob. 7E Ch. 3.10 - Prob. 8E Ch. 3.10 - Prob. 9E Ch. 3.10 - Prob. 10E Ch. 3.10 - Prob. 11E Ch. 3.10 - Prob. 12E Ch. 3.10 - Prob. 13E Ch. 3.10 - Prob. 14E Ch. 3.10 - Prob. 15E Ch. 3.10 - Prob. 16E Ch. 3.10 - Prob. 17E Ch. 3.10 - Prob. 18E Ch. 3.10 - Prob. 19E Ch. 3.10 - Prob. 20E Ch. 3.10 - Prob. 21E Ch. 3.10 - Prob. 22E Ch. 3.10 - Prob. 23E Ch. 3.10 - Prob. 24E Ch. 3.10 - Prob. 25E Ch. 3.10 - Prob. 26E Ch. 3.10 - Prob. 27E Ch. 3.10 - Prob. 28E Ch. 3.10 - Prob. 29E Ch. 3.10 - Prob. 30E Ch. 3.10 - Prob. 31E Ch. 3.10 - Prob. 32E Ch. 3.10 - Prob. 33E Ch. 3.10 - Prob. 34E Ch. 3.10 - Prob. 35E Ch. 3.10 - Prob. 36E Ch. 3.10 - Prob. 37E Ch. 3.10 - Prob. 38E Ch. 3.10 - Prob. 39E Ch. 3.10 - Prob. 40E Ch. 3.10 - Prob. 41E Ch. 3.10 - Prob. 42E Ch. 3.10 - Prob. 43E Ch. 3.10 - Prob. 44E Ch. 3.10 - Prob. 45E Ch. 3 - Prob. 1CRE Ch. 3 - Prob. 2CRE Ch. 3 - Prob. 3CRE Ch. 3 - Prob. 4CRE Ch. 3 - Prob. 5CRE Ch. 3 - Prob. 6CRE Ch. 3 - Prob. 7CRE Ch. 3 - Prob. 8CRE Ch. 3 - Prob. 9CRE Ch. 3 - Prob. 10CRE Ch. 3 - Prob. 11CRE Ch. 3 - Prob. 12CRE Ch. 3 - Prob. 13CRE Ch. 3 - Prob. 14CRE Ch. 3 - Prob. 15CRE Ch. 3 - Prob. 16CRE Ch. 3 - Prob. 17CRE Ch. 3 - Prob. 18CRE Ch. 3 - Prob. 19CRE Ch. 3 - Prob. 20CRE Ch. 3 - Prob. 21CRE Ch. 3 - Prob. 22CRE Ch. 3 - Prob. 23CRE Ch. 3 - Prob. 24CRE Ch. 3 - Prob. 25CRE Ch. 3 - Prob. 26CRE Ch. 3 - Prob. 27CRE Ch. 3 - Prob. 28CRE Ch. 3 - Prob. 29CRE Ch. 3 - Prob. 30CRE Ch. 3 - Prob. 31CRE Ch. 3 - Prob. 32CRE Ch. 3 - Prob. 33CRE Ch. 3 - Prob. 34CRE Ch. 3 - Prob. 35CRE Ch. 3 - Prob. 36CRE Ch. 3 - Prob. 37CRE Ch. 3 - Prob. 38CRE Ch. 3 - Prob. 39CRE Ch. 3 - Prob. 40CRE Ch. 3 - Prob. 41CRE Ch. 3 - Prob. 42CRE Ch. 3 - Prob. 43CRE Ch. 3 - Prob. 44CRE Ch. 3 - Prob. 45CRE Ch. 3 - Prob. 46CRE Ch. 3 - Prob. 47CRE Ch. 3 - Prob. 48CRE Ch. 3 - Prob. 49CRE Ch. 3 - Prob. 50CRE Ch. 3 - Prob. 51CRE Ch. 3 - Prob. 52CRE Ch. 3 - Prob. 53CRE Ch. 3 - Prob. 54CRE Ch. 3 - Prob. 55CRE Ch. 3 - Prob. 56CRE Ch. 3 - Prob. 57CRE Ch. 3 - Prob. 58CRE Ch. 3 - Prob. 59CRE Ch. 3 - Prob. 60CRE Ch. 3 - Prob. 61CRE Ch. 3 - Prob. 62CRE Ch. 3 - Prob. 63CRE Ch. 3 - Prob. 64CRE Ch. 3 - Prob. 65CRE Ch. 3 - Prob. 66CRE Ch. 3 - Prob. 67CRE Ch. 3 - Prob. 68CRE Ch. 3 - Prob. 69CRE Ch. 3 - Prob. 70CRE Ch. 3 - Prob. 71CRE Ch. 3 - Prob. 72CRE Ch. 3 - Prob. 73CRE Ch. 3 - Prob. 74CRE Ch. 3 - Prob. 75CRE Ch. 3 - Prob. 76CRE Ch. 3 - Prob. 77CRE Ch. 3 - Prob. 78CRE Ch. 3 - Prob. 79CRE Ch. 3 - Prob. 80CRE Ch. 3 - Prob. 81CRE Ch. 3 - Prob. 82CRE Ch. 3 - Prob. 83CRE Ch. 3 - Prob. 84CRE Ch. 3 - Prob. 85CRE Ch. 3 - Prob. 86CRE Ch. 3 - Prob. 87CRE Ch. 3 - Prob. 88CRE Ch. 3 - Prob. 89CRE Ch. 3 - Prob. 90CRE Ch. 3 - Prob. 91CRE Ch. 3 - Prob. 92CRE Ch. 3 - Prob. 93CRE Ch. 3 - Prob. 94CRE Ch. 3 - Prob. 95CRE Ch. 3 - Prob. 96CRE Ch. 3 - Prob. 97CRE Ch. 3 - Prob. 98CRE Ch. 3 - Prob. 99CRE Ch. 3 - Prob. 100CRE Ch. 3 - Prob. 101CRE Ch. 3 - Prob. 102CRE Ch. 3 - Prob. 103CRE Ch. 3 - Prob. 104CRE Ch. 3 - Prob. 105CRE Ch. 3 - Prob. 106CRE Ch. 3 - Prob. 107CRE Ch. 3 - Prob. 108CRE Ch. 3 - Prob. 109CRE Ch. 3 - Prob. 110CRE Ch. 3 - Prob. 111CRE Ch. 3 - Prob. 112CRE Ch. 3 - Prob. 113CRE Ch. 3 - Prob. 114CRE Ch. 3 - Prob. 115CRE Ch. 3 - Prob. 116CRE Ch. 3 - Prob. 117CRE Ch. 3 - Prob. 118CRE Ch. 3 - Prob. 119CRE Ch. 3 - Prob. 120CRE

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the equation of the tangent line at the indicated point θ = π 4 .

Solution Summary: The author calculates the equation of the tangent line at the indicated point theta =pi4.

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To find: the equation of the tangent line at the indicated point θ=π4.

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Chapter 3 Solutions