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4-x² 4. Evaluate [*, [* (r² + y°) dz dy dx. 4-. Hint: This iterated integral is a triple integral over the solid region E = {(x, y, z) | –2

4-x² 4. Evaluate [*, [* (r² + y°) dz dy dx. 4-. Hint: This iterated integral is a triple integral over the solid region E = {(x, y, z) | –2

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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1. (a) Plot the point with cylindrical coordinates (2, 27/3, 1) and find its rectangular coordinates. (b) Find cylindrical coordinates of the point with rectangular coordinates (3, – 3, –7). 2. The point (0, 2 /3, –2) is given in rectangular coordinates. Find spheri cal coordinates for this point. 3. The point (2, T/4, 7/3) is given in spherical coordinates. Plot the point and find its rectangular coordinates. V4-x² 4. Evaluate ", L(r² + y®) dz dy dx. -2 4-x2 Hint: This iterated integral is a triple integral over the solid region z=Vx²+y? E = {(x, y, z) | –2 < x< 2, -/4 – x² < y< /4 – x², Vx² + y² < z < 2} and the projection of E onto the xy-plane is the disk x² + y² < 4. The lower surface of E is the cone z = 2 Vx² + y² and its upper surface is the plane z = 2. (See Figure 9.) This region has a much simpler description in cylindrical coordinates: FIGURE 9
Transcribed Image Text:1. (a) Plot the point with cylindrical coordinates (2, 27/3, 1) and find its rectangular coordinates. (b) Find cylindrical coordinates of the point with rectangular coordinates (3, – 3, –7). 2. The point (0, 2 /3, –2) is given in rectangular coordinates. Find spheri cal coordinates for this point. 3. The point (2, T/4, 7/3) is given in spherical coordinates. Plot the point and find its rectangular coordinates. V4-x² 4. Evaluate ", L(r² + y®) dz dy dx. -2 4-x2 Hint: This iterated integral is a triple integral over the solid region z=Vx²+y? E = {(x, y, z) | –2 < x< 2, -/4 – x² < y< /4 – x², Vx² + y² < z < 2} and the projection of E onto the xy-plane is the disk x² + y² < 4. The lower surface of E is the cone z = 2 Vx² + y² and its upper surface is the plane z = 2. (See Figure 9.) This region has a much simpler description in cylindrical coordinates: FIGURE 9
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