1 Functions 2 Limits And Continuity 3 Derivatives 4 Application Of Derivatives 5 Integrals 6 Applications Of Definite Integrals 7 Integrals And Trascendental Functions 8 Techniques Of Integration 9 Infinite Sequences And Series 10 Parametric Equations And Polar Coordinates 11 Vectors And The Geometry Of Space 12 Vector-valued Functions And Motion In Space 13 Partial Derivatives 14 Multiple Integrals 15 Integrals And Vector Fields 16 First-order Differential Equations 17 Second-order Differential Equations A.1 Real Numbers And The Real Line A.2 Mathematical Induction A.3 Lines And Circles A.4 Conic Sections A.5 Proofs Of Limit Theorems A.6 Commonly Occurring Limits A.7 Theory Of The Real Numbers A.8 Complex Numbers A.9 The Distributive Law For Vector Cross Products A.10 The Mixed Derivative Theorem And The Increment Theorem B.1 Relative Rates Of Growth B.2 Probability B.3 Conics In Polar Coordinates B.4 Taylor's Formula For Two Variables B.5 Partial Derivatives With Constrained Variables expand_more
14.1 Double And Iterated Integrals Over Rectangles 14.2 Double Integrals Over General Regions 14.3 Area By Double Integration 14.4 Double Integrals In Polar Form 14.5 Triple Integrals In Rectangular Coordinates 14.6 Applications 14.7 Triple Integrals In Cylindrical And Spherical Coordinates 14.8 Substitution In Multiple Integrals Chapter Questions expand_more
Problem 1E: In Exercises 1-8, describe the given region in polar coordinates.
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Problem 2E: In Exercises 1-8, describe the given region in polar coordinates. 2. Problem 3E: In Exercises 1-8, describe the given region in polar coordinates.
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Problem 4E: In Exercises 1-8, describe the given region in polar coordinates.
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Problem 5E: In Exercises 1-8, describe the given region in polar coordinates.
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Problem 6E: In Exercises 1-8, describe the given region in polar coordinates.
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Problem 7E: In Exercises 1-8, describe the given region in polar coordinates.
7. The region enclosed by the... Problem 8E: In Exercises 1-8, describe the given region in polar coordinates.
8. The region enclosed by the... Problem 9E:
In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 10E: In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 11E: In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 12E: In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 13E: In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 14E: In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 15E: In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 16E: In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 17E: In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 18E Problem 19E: In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 20E Problem 21E: In Exercises 9–22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 22E: In Exercises 9–22, change the Cartesian integral into an equivalent polar integral. Then evaluate... Problem 23E: In Exercises 23-26, sketch the region of integration, and convert each polar integral or sum of... Problem 24E: In Exercises 23–26, sketch the region of integration, and convert each polar integral or sum of... Problem 25E: In Exercises 23–26, sketch the region of integration, and convert each polar integral or sum of... Problem 26E: In Exercises 23–26, sketch the region of integration, and convert each polar integral or sum of... Problem 27E: Find the area of the region cut from the first quadrant by the curve r = 2(2 − sin 2θ)1/2.
Problem 28E Problem 29E: One leaf of a rose Find the area enclosed by one leaf of the rose r = 12 cos 3θ.
Problem 30E Problem 31E Problem 32E: Overlapping cardioids Find the area of the region common to the interiors of the cardioids r = 1 +... Problem 33E: In polar coordinates, the average value of a function over a region R (Section 14.3) is given... Problem 34E Problem 35E: In polar coordinates, the average value of a function over a region R (Section 14.3) is given... Problem 36E Problem 37E: Converting to a polar integral Integrate over the region
Problem 38E Problem 39E: Volume of noncircular right cylinder The region that lies inside the cardioid r = 1 + cos θ and... Problem 40E Problem 41E Problem 42E Problem 43E Problem 44E: Area formula in polar coordinates Use the double integral in polar coordinates to derive the... Problem 45E Problem 46E Problem 47E: Evaluate the integral , where R is the region inside the upper semicircle of radius 2 centered at... Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E format_list_bulleted