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Math Calculus Calculus

To prove: The function f ( x ) = cot x is one-to-one on the interval ( 0 , π ) and therefore has an inverse function on that interval.

To prove: The function f ( x ) = cot x is one-to-one on the interval ( 0 , π ) and therefore has an inverse function on that interval.

Solution Summary: The author explains that the function f(x)=mathrmcotx is one-to-one on the interval (0,pi ) and therefore has an inverse function

Calculus

10th Edition

ISBN: 9781285057095

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 5.3, Problem 32E

To determine

To prove: The function f(x)=cotx is one-to-one on the interval (0,π) and therefore has an inverse function on that interval.

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Chapter 5.3, Problem 31E

Chapter 5.3, Problem 33E

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The graph shows the temperature...Ch. 5.1 - Prob. 99E Ch. 5.1 - Prob. 100E Ch. 5.1 - Prob. 101E Ch. 5.1 - Prob. 102E Ch. 5.1 - Home Mortgage The term t (in years) of a $200,000...Ch. 5.1 - Prob. 104E Ch. 5.1 - Modeling Data The table shows the temperatures T...Ch. 5.1 - Modeling Data The atmospheric pressure decreases...Ch. 5.1 - Tractrix A person walking along a dock drags a...Ch. 5.1 - Prob. 108E Ch. 5.1 - Prob. 109E Ch. 5.2 - Prob. 1E Ch. 5.2 - Finding an Indefinite Integral In Exercises 126,...Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Prob. 21E Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - 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Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Prob. 79E Ch. 5.5 - Prob. 80E Ch. 5.5 - Prob. 81E Ch. 5.5 - Prob. 82E Ch. 5.5 - Prob. 83E Ch. 5.5 - Prob. 84E Ch. 5.5 - Prob. 85E Ch. 5.5 - Prob. 86E Ch. 5.5 - Prob. 87E Ch. 5.5 - Depreciation After t years, the value of a car...Ch. 5.5 - Prob. 89E Ch. 5.5 - Prob. 90E Ch. 5.5 - Prob. 91E Ch. 5.5 - Prob. 92E Ch. 5.5 - Prob. 93E Ch. 5.5 - Prob. 94E Ch. 5.5 - Prob. 95E Ch. 5.5 - Prob. 96E Ch. 5.5 - Prob. 97E Ch. 5.5 - Prob. 98E Ch. 5.5 - Timber Yield The yield V (in millions of cubic...Ch. 5.5 - Prob. 100E Ch. 5.5 - Prob. 101E Ch. 5.5 - Modeling Data The breaking strengths B (in tons)...Ch. 5.5 - Prob. 103E Ch. 5.5 - Prob. 104E Ch. 5.5 - Prob. 105E Ch. 5.5 - Prob. 106E Ch. 5.5 - Prob. 107E Ch. 5.5 - Prob. 108E Ch. 5.5 - Prob. 109E Ch. 5.5 - Prob. 110E Ch. 5.5 - Prob. 111E Ch. 5.5 - Prob. 112E Ch. 5.5 - Prob. 113E Ch. 5.5 - Prob. 114E Ch. 5.5 - Prob. 115E Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - Prob. 117E Ch. 5.5 - Prob. 118E Ch. 5.5 - Prob. 119E Ch. 5.5 - Prob. 120E Ch. 5.5 - Prob. 121E Ch. 5.5 - Prob. 122E Ch. 5.5 - Prob. 123E Ch. 5.6 - Restricted Domain What is a restricted domain? Why...Ch. 5.6 - Prob. 1E Ch. 5.6 - Prob. 2E Ch. 5.6 - Prob. 3E Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Prob. 5E Ch. 5.6 - Prob. 6E Ch. 5.6 - Prob. 7E Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Prob. 9E Ch. 5.6 - Prob. 10E Ch. 5.6 - Prob. 11E Ch. 5.6 - Approximating Inverse Trigonometric Functions In...Ch. 5.6 - Approximating Inverse Trigonometric Functions In...Ch. 5.6 - Prob. 14E Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Prob. 16E Ch. 5.6 - Prob. 17E Ch. 5.6 - Prob. 18E Ch. 5.6 - Prob. 19E Ch. 5.6 - Prob. 20E Ch. 5.6 - Prob. 21E Ch. 5.6 - Prob. 22E Ch. 5.6 - Prob. 23E Ch. 5.6 - Prob. 24E Ch. 5.6 - Prob. 25E Ch. 5.6 - Prob. 26E Ch. 5.6 - Prob. 27E Ch. 5.6 - Prob. 28E Ch. 5.6 - Prob. 29E Ch. 5.6 - Prob. 30E Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Prob. 32E Ch. 5.6 - Prob. 33E Ch. 5.6 - Prob. 34E Ch. 5.6 - Prob. 35E Ch. 5.6 - Solving an Equation In Exercises 37-40, solve the...Ch. 5.6 - Prob. 37E Ch. 5.6 - Prob. 38E Ch. 5.6 - Prob. 39E Ch. 5.6 - Prob. 40E Ch. 5.6 - Prob. 41E Ch. 5.6 - Prob. 42E Ch. 5.6 - Prob. 43E Ch. 5.6 - Prob. 44E Ch. 5.6 - Prob. 45E Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Prob. 47E Ch. 5.6 - Prob. 48E Ch. 5.6 - Prob. 49E Ch. 5.6 - Prob. 54E Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Prob. 51E Ch. 5.6 - Prob. 52E Ch. 5.6 - Prob. 53E Ch. 5.6 - Prob. 55E Ch. 5.6 - Prob. 56E Ch. 5.6 - Prob. 57E Ch. 5.6 - Prob. 58E Ch. 5.6 - Prob. 59E Ch. 5.6 - Prob. 60E Ch. 5.6 - Prob. 61E Ch. 5.6 - Prob. 62E Ch. 5.6 - Prob. 63E Ch. 5.6 - Prob. 64E Ch. 5.6 - Finding Relative Extrema In Exercises 63-66, find...Ch. 5.6 - Finding Relative Extrema In Exercises 63-66, find...Ch. 5.6 - Prob. 71E Ch. 5.6 - Prob. 72E Ch. 5.6 - Prob. 73E Ch. 5.6 - Prob. 74E Ch. 5.6 - Prob. 75E Ch. 5.6 - Prob. 76E Ch. 5.6 - Prob. 77E Ch. 5.6 - Prob. 78E Ch. 5.6 - Prob. 79E Ch. 5.6 - Prob. 80E Ch. 5.6 - Prob. 83E Ch. 5.6 - Prob. 84E Ch. 5.6 - Prob. 82E Ch. 5.6 - Prob. 87E Ch. 5.6 - Prob. 88E Ch. 5.6 - Prob. 89E Ch. 5.6 - True or False? In Exercises 83-86, determine...Ch. 5.6 - Prob. 85E Ch. 5.6 - Prob. 86E Ch. 5.6 - Linear and Quadratic Approximations In Exercises...Ch. 5.6 - Prob. 66E Ch. 5.6 - Prob. 67E Ch. 5.6 - Prob. 68E Ch. 5.6 - Angular Rate of Change An airplane flies at an...Ch. 5.6 - Prob. 92E Ch. 5.6 - Angular Rate of Change In a free-fall experiment,...Ch. 5.6 - Angular Rate of Change A television camera at...Ch. 5.6 - Maximizing an Angle A billboard 85 feet wide is...Ch. 5.6 - Angular Speed A patrol car is parked 50 feet from...Ch. 5.6 - Prob. 97E Ch. 5.6 - Prob. 98E Ch. 5.6 - Prob. 99E Ch. 5.6 - Prob. 100E Ch. 5.6 - Maximizing an Angle In the figure, find the value...Ch. 5.6 - Prob. 102E Ch. 5.6 - Prob. 103E Ch. 5.6 - Prob. 104E Ch. 5.7 - Prob. 1E Ch. 5.7 - Prob. 2E Ch. 5.7 - Prob. 3E Ch. 5.7 - Prob. 4E Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 120,...Ch. 5.7 - Prob. 7E Ch. 5.7 - Prob. 8E Ch. 5.7 - Prob. 9E Ch. 5.7 - Prob. 10E Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Prob. 12E Ch. 5.7 - Prob. 13E Ch. 5.7 - Prob. 14E Ch. 5.7 - Prob. 15E Ch. 5.7 - Prob. 16E Ch. 5.7 - Prob. 17E Ch. 5.7 - Prob. 18E Ch. 5.7 - Prob. 19E Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Prob. 21E Ch. 5.7 - Prob. 22E Ch. 5.7 - Prob. 23E Ch. 5.7 - Prob. 24E Ch. 5.7 - Prob. 25E Ch. 5.7 - Prob. 26E Ch. 5.7 - Prob. 27E Ch. 5.7 - Prob. 28E Ch. 5.7 - Prob. 29E Ch. 5.7 - Prob. 30E Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Prob. 33E Ch. 5.7 - Prob. 34E Ch. 5.7 - Prob. 35E Ch. 5.7 - Prob. 36E Ch. 5.7 - Prob. 37E Ch. 5.7 - Prob. 38E Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Prob. 40E Ch. 5.7 - Prob. 41E Ch. 5.7 - Prob. 42E Ch. 5.7 - Prob. 43E Ch. 5.7 - Prob. 44E Ch. 5.7 - Prob. 45E Ch. 5.7 - Prob. 46E Ch. 5.7 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.7 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.7 - Prob. 49E Ch. 5.7 - Prob. 50E Ch. 5.7 - Prob. 51E Ch. 5.7 - Prob. 52E Ch. 5.7 - Prob. 53E Ch. 5.7 - Prob. 54E Ch. 5.7 - Prob. 55E Ch. 5.7 - Prob. 56E Ch. 5.7 - Prob. 57E Ch. 5.7 - Prob. 58E Ch. 5.7 - Prob. 59E Ch. 5.7 - Prob. 60E Ch. 5.7 - Prob. 61E Ch. 5.7 - Prob. 62E Ch. 5.7 - Prob. 63E Ch. 5.7 - Prob. 64E Ch. 5.7 - Area In Exercises 63-66, find the area of the...Ch. 5.7 - Prob. 66E Ch. 5.7 - Prob. 67E Ch. 5.7 - Prob. 68E Ch. 5.7 - Prob. 69E Ch. 5.7 - Prob. 70E Ch. 5.7 - Prob. 71E Ch. 5.7 - Prob. 72E Ch. 5.7 - Prob. 73E Ch. 5.7 - True or False? In Exercises 7174, determine...Ch. 5.7 - Prob. 75E Ch. 5.7 - Prob. 76E Ch. 5.7 - Prob. 77E Ch. 5.7 - Prob. 78E Ch. 5.7 - Prob. 79E Ch. 5.7 - Prob. 80E Ch. 5.8 - Prob. 1E Ch. 5.8 - Prob. 2E Ch. 5.8 - Prob. 3E Ch. 5.8 - Prob. 4E Ch. 5.8 - Prob. 5E Ch. 5.8 - Prob. 6E Ch. 5.8 - Prob. 7E Ch. 5.8 - Verifying an Identity In Exercises 11-18, verify...Ch. 5.8 - Prob. 9E Ch. 5.8 - Prob. 10E Ch. 5.8 - Prob. 11E Ch. 5.8 - Prob. 12E Ch. 5.8 - Prob. 13E Ch. 5.8 - Prob. 14E Ch. 5.8 - Prob. 15E Ch. 5.8 - Prob. 16E Ch. 5.8 - Prob. 17E Ch. 5.8 - Prob. 18E Ch. 5.8 - Prob. 19E Ch. 5.8 - Finding a Limit In Exercises 1722, find the limit....Ch. 5.8 - Prob. 21E Ch. 5.8 - Finding a Limit In Exercises 21-24, find the...Ch. 5.8 - Prob. 23E Ch. 5.8 - Prob. 24E Ch. 5.8 - Prob. 25E Ch. 5.8 - Prob. 26E Ch. 5.8 - Prob. 27E Ch. 5.8 - Prob. 28E Ch. 5.8 - Prob. 29E Ch. 5.8 - Prob. 30E Ch. 5.8 - Prob. 31E Ch. 5.8 - Prob. 32E Ch. 5.8 - Prob. 33E Ch. 5.8 - Prob. 34E Ch. 5.8 - Prob. 35E Ch. 5.8 - Prob. 36E Ch. 5.8 - Finding Relative Extrema In Exercises 39-42, find...Ch. 5.8 - Prob. 38E Ch. 5.8 - Prob. 39E Ch. 5.8 - Prob. 40E Ch. 5.8 - Prob. 41E Ch. 5.8 - Prob. 42E Ch. 5.8 - Prob. 43E Ch. 5.8 - Prob. 44E Ch. 5.8 - Prob. 45E Ch. 5.8 - Prob. 46E Ch. 5.8 - Prob. 47E Ch. 5.8 - Prob. 48E Ch. 5.8 - Prob. 49E Ch. 5.8 - Prob. 50E Ch. 5.8 - Prob. 53E Ch. 5.8 - Prob. 51E Ch. 5.8 - Finding an Indefinite Integral In Exercises 4354,...Ch. 5.8 - Prob. 52E Ch. 5.8 - Prob. 55E Ch. 5.8 - Prob. 56E Ch. 5.8 - Prob. 57E Ch. 5.8 - Prob. 58E Ch. 5.8 - Prob. 59E Ch. 5.8 - Prob. 60E Ch. 5.8 - Prob. 61E Ch. 5.8 - Prob. 62E Ch. 5.8 - Prob. 63E Ch. 5.8 - Prob. 64E Ch. 5.8 - Prob. 65E Ch. 5.8 - Prob. 66E Ch. 5.8 - Prob. 67E Ch. 5.8 - Prob. 68E Ch. 5.8 - Prob. 69E Ch. 5.8 - Prob. 70E Ch. 5.8 - Prob. 71E Ch. 5.8 - Prob. 72E Ch. 5.8 - Prob. 73E Ch. 5.8 - Prob. 74E Ch. 5.8 - Prob. 75E Ch. 5.8 - Prob. 76E Ch. 5.8 - Finding an Indefinite Integral In Exercises 75-82,...Ch. 5.8 - Finding an Indefinite Integral In Exercises 75-82,...Ch. 5.8 - Prob. 79E Ch. 5.8 - Prob. 80E Ch. 5.8 - Prob. 81E Ch. 5.8 - Prob. 82E Ch. 5.8 - Prob. 83E Ch. 5.8 - Prob. 84E Ch. 5.8 - Prob. 85E Ch. 5.8 - Prob. 86E Ch. 5.8 - Differential Equation In Exercises 8790, solve the...Ch. 5.8 - Differential Equation In Exercises 8790, solve the...Ch. 5.8 - Differential Equation In Exercises 87 and 88, find...Ch. 5.8 - Differential Equation In Exercises 87 and 88, find...Ch. 5.8 - Area In Exercises 89-92, find the area of the...Ch. 5.8 - Area In Exercises 8992, find the area of the given...Ch. 5.8 - Prob. 93E Ch. 5.8 - Prob. 94E Ch. 5.8 - Prob. 95E Ch. 5.8 - Prob. 96E Ch. 5.8 - Tractrix Consider the equation of a tractrix...Ch. 5.8 - Prob. 98E Ch. 5.8 - Prob. 99E Ch. 5.8 - Prob. 100E Ch. 5.8 - Prob. 101E Ch. 5.8 - Prob. 102E Ch. 5.8 - Prob. 103E Ch. 5.8 - Prob. 104E Ch. 5.8 - Prob. 105E Ch. 5.8 - Prob. 106E Ch. 5.8 - Verifying a Differentiation Formula In Exercises...Ch. 5.8 - Prob. 108E Ch. 5.8 - Prob. 109E Ch. 5.8 - PUTNAM EXAM CHALLENGE Prove or disprove: there is...Ch. 5 - Sketching a Graph In Exercises 1 and 2, sketch the...Ch. 5 - Prob. 2RE Ch. 5 - Prob. 3RE Ch. 5 - Prob. 4RE Ch. 5 - Prob. 5RE Ch. 5 - Prob. 6RE Ch. 5 - Prob. 7RE Ch. 5 - Prob. 8RE Ch. 5 - Prob. 9RE Ch. 5 - Prob. 10RE Ch. 5 - Prob. 11RE Ch. 5 - Prob. 12RE Ch. 5 - Prob. 13RE Ch. 5 - Prob. 14RE Ch. 5 - Prob. 15RE Ch. 5 - Prob. 16RE Ch. 5 - Prob. 17RE Ch. 5 - Finding an Indefinite Integral In Exercises 21-26,...Ch. 5 - Prob. 19RE Ch. 5 - Prob. 20RE Ch. 5 - Prob. 21RE Ch. 5 - Prob. 22RE Ch. 5 - Prob. 23RE Ch. 5 - Prob. 24RE Ch. 5 - Prob. 25RE Ch. 5 - Prob. 26RE Ch. 5 - Prob. 27RE Ch. 5 - Prob. 28RE Ch. 5 - Evaluating the Derivative of an Inverse Function...Ch. 5 - Prob. 30RE Ch. 5 - Prob. 31RE Ch. 5 - Prob. 32RE Ch. 5 - Prob. 33RE Ch. 5 - Prob. 34RE Ch. 5 - Prob. 35RE Ch. 5 - Prob. 36RE Ch. 5 - Prob. 37RE Ch. 5 - Prob. 38RE Ch. 5 - Prob. 39RE Ch. 5 - Prob. 40RE Ch. 5 - Prob. 41RE Ch. 5 - Prob. 42RE Ch. 5 - Prob. 43RE Ch. 5 - Prob. 44RE Ch. 5 - Prob. 45RE Ch. 5 - Prob. 46RE Ch. 5 - Prob. 47RE Ch. 5 - Prob. 48RE Ch. 5 - Prob. 49RE Ch. 5 - Prob. 50RE Ch. 5 - Prob. 51RE Ch. 5 - Prob. 52RE Ch. 5 - Prob. 53RE Ch. 5 - Prob. 54RE Ch. 5 - Prob. 55RE Ch. 5 - Prob. 56RE Ch. 5 - Prob. 57RE Ch. 5 - Prob. 58RE Ch. 5 - Prob. 59RE Ch. 5 - Prob. 60RE Ch. 5 - Prob. 61RE Ch. 5 - Prob. 62RE Ch. 5 - Prob. 63RE Ch. 5 - Prob. 64RE Ch. 5 - Prob. 65RE Ch. 5 - Prob. 66RE Ch. 5 - Prob. 68RE Ch. 5 - Prob. 67RE Ch. 5 - Prob. 69RE Ch. 5 - Prob. 70RE Ch. 5 - Prob. 71RE Ch. 5 - Prob. 72RE Ch. 5 - Finding a Derivative In Exercises 99-104, find the...Ch. 5 - Prob. 74RE Ch. 5 - Prob. 75RE Ch. 5 - Prob. 76RE Ch. 5 - Prob. 77RE Ch. 5 - Prob. 78RE Ch. 5 - Prob. 79RE Ch. 5 - Prob. 80RE Ch. 5 - Prob. 81RE Ch. 5 - Prob. 82RE Ch. 5 - Prob. 83RE Ch. 5 - Prob. 84RE Ch. 5 - Prob. 85RE Ch. 5 - Prob. 86RE Ch. 5 - Prob. 87RE Ch. 5 - Prob. 88RE Ch. 5 - Prob. 89RE Ch. 5 - Prob. 90RE Ch. 5 - Prob. 91RE Ch. 5 - Prob. 92RE Ch. 5 - Prob. 93RE Ch. 5 - Prob. 94RE Ch. 5 - Prob. 95RE Ch. 5 - Prob. 96RE Ch. 5 - Prob. 1PS Ch. 5 - Prob. 2PS Ch. 5 - Prob. 3PS Ch. 5 - Prob. 4PS Ch. 5 - Prob. 5PS Ch. 5 - Prob. 6PS Ch. 5 - Prob. 7PS Ch. 5 - Decreasing Function Show that f(x)=lnxnx is a...Ch. 5 - Prob. 9PS Ch. 5 - Prob. 10PS Ch. 5 - Prob. 11PS Ch. 5 - Gudermannian Function The Gudcrmannian function of...Ch. 5 - Area Use integration by substitution to find the...Ch. 5 - Prob. 14PS Ch. 5 - Prob. 15PS Ch. 5 - Prob. 16PS

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