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Identify the surfaces of the following equations by converting them into equations in the Cartesian form. Show your complete solutions. (a) ² = 4 + 4r² (b) psin osin

Identify the surfaces of the following equations by converting them into equations in the Cartesian form. Show your complete solutions. (a) ² = 4 + 4r² (b) psin osin

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Directions: Solve the following problems NEATLY, COMPLETELY and CORRECTLY. You must submit the problem set through Canvas in PDF file. Do NOT use graphing devices in your work. 1. Identify the surfaces of the following equations by converting them into equations in the Cartesian form. Show your complete solutions. (a) ² = 4 + 4² (b) p = sin sine 2. Evaluate the double integral that will find the volume of a solid bounded by 1-2y²-3² and the zy- plane. (Hint: Use trigonometric substitution to evaluate the formulated double integral.) 3. Set-up the iterated double integral in polar coordinates that gives the volume of the solid enclosed by the hyperboloid = = √√1+ + and under the plane z = 5. 4. Evaluate the double integral: So de dy. (Hint: Change the order of integration to dy dr.) 5. Use Cartesian coordinates to evaluate JJ v av dV where D is the tetrahedron in the first octant bounded by the coordinate planes and the plane 2x + 3y +z = 6. Use dV= dz dy dr. Draw the solid D. 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical coordinates with dV = r dz dr de where R:0≤ 2≤ 1,0 ≤ y ≤ √1-2², 0≤ ≤ √√4-(2²+ y²). Draw the solid R. (b) the volume of the solid B that lies above the cone z = √√/32² + 3y² and below the sphere a² + y² +2²= z using spherical coordinates. Draw the solid B
Transcribed Image Text:Directions: Solve the following problems NEATLY, COMPLETELY and CORRECTLY. You must submit the problem set through Canvas in PDF file. Do NOT use graphing devices in your work. 1. Identify the surfaces of the following equations by converting them into equations in the Cartesian form. Show your complete solutions. (a) ² = 4 + 4² (b) p = sin sine 2. Evaluate the double integral that will find the volume of a solid bounded by 1-2y²-3² and the zy- plane. (Hint: Use trigonometric substitution to evaluate the formulated double integral.) 3. Set-up the iterated double integral in polar coordinates that gives the volume of the solid enclosed by the hyperboloid = = √√1+ + and under the plane z = 5. 4. Evaluate the double integral: So de dy. (Hint: Change the order of integration to dy dr.) 5. Use Cartesian coordinates to evaluate JJ v av dV where D is the tetrahedron in the first octant bounded by the coordinate planes and the plane 2x + 3y +z = 6. Use dV= dz dy dr. Draw the solid D. 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical coordinates with dV = r dz dr de where R:0≤ 2≤ 1,0 ≤ y ≤ √1-2², 0≤ ≤ √√4-(2²+ y²). Draw the solid R. (b) the volume of the solid B that lies above the cone z = √√/32² + 3y² and below the sphere a² + y² +2²= z using spherical coordinates. Draw the solid B
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