Explanation Given data: The given inequality polar expression is written as follows: 0 ≤ r ≤ 2 − 2 cos θ Description: Condition for symmetric about the x -axis: If the point ( r , θ ) lies on a curve, then the point ( r , − θ ) or ( − r , π − θ ) also lies on the curve in order to satisfy the condition for symmetric about the x -axis. Condition for symmetric about the y -axis: If the point ( r , θ ) lies on a curve, then the point ( r , π − θ ) or ( − r , − θ ) also lies on the curve in order to satisfy the condition for symmetric about the y -axis. Condition for symmetric about the origin: If the point ( r , θ ) lies on a curve, then the point ( − r , θ ) or ( − r , θ + π ) also lies on the curve in order to satisfy the condition for symmetric about the origin. Consider r = 2 − 2 cos θ to sketch the required region. Rewrite the given polar coordinate equation as follows: r = 2 − 2 cos θ (1) Substitute ( r , θ ) in the Equation (1) as follows: r = 2 − 2 cos θ (2) Substitute ( r , − θ ) in the Equation (1) as follows: r = 2 − 2 cos ( − θ ) r = 2 − 2 cos θ { ∵ cos ( − θ ) = cos θ } (3) As expressions in Equation (2) and (3) are same, both the points ( r , θ ) and ( r , − θ ) lies on the given curve

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 10.4, Problem 31E

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Sketch the region for the given inequality polar expression.

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Chapter 10.4, Problem 30E

Chapter 10.4, Problem 32E

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University Calculus: Early Transcendentals (4th Edition)

Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric...

Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Prob. 12E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Prob. 14E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - In Exercises 25–28, use the given graphs of x =...Ch. 10.1 - Finding Parametric Equations Find parametric...Ch. 10.1 - Find parametric equations and a parameter interval...Ch. 10.1 - Prob. 31E Ch. 10.1 - In Exercises 31–36, find a parametrization for the...Ch. 10.1 - 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Finding Polar Areas Find the areas of the regions...Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E Ch. 10.5 - Prob. 7E Ch. 10.5 - Prob. 8E Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Prob. 12E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.5 - Prob. 16E Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Prob. 19E Ch. 10.5 - Prob. 20E Ch. 10.5 - Find the lengths of the curves in Exercises 2128....Ch. 10.5 - Prob. 22E Ch. 10.5 - Prob. 23E Ch. 10.5 - Prob. 24E Ch. 10.5 - Prob. 25E Ch. 10.5 - Prob. 26E Ch. 10.5 - Find the lengths of the curves in Exercises 2128....Ch. 10.5 - Prob. 28E Ch. 10.5 - Prob. 29E Ch. 10.5 - Prob. 30E Ch. 10.5 - Prob. 31E Ch. 10.5 - Prob. 32E Ch. 10 - Prob. 1GYR Ch. 10 - Prob. 2GYR Ch. 10 - Prob. 3GYR Ch. 10 - Prob. 4GYR Ch. 10 - Prob. 5GYR Ch. 10 - 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