Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z = √3x² + 3y². (a) Sketch the solid region E. (b) Sketch the cross section of E in the yz-plane (when x=0). Shade the region. (c) Sketch the projection of the solid onto the xy-plane. Shade the region. (d) SET UP but do not evaluate the integral in cylindrical coordinates (dz dr de) that gives the volume of E. Indicate how you found the limits of integration for z, r, and 0. (e) SET UP but do not evaluate the integral in spherical coordinates (dp do do) that gives the volume of E. Indicate how you found the limits of integration for p, , and 0. a)
Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z = √3x² + 3y². (a) Sketch the solid region E. (b) Sketch the cross section of E in the yz-plane (when x=0). Shade the region. (c) Sketch the projection of the solid onto the xy-plane. Shade the region. (d) SET UP but do not evaluate the integral in cylindrical coordinates (dz dr de) that gives the volume of E. Indicate how you found the limits of integration for z, r, and 0. (e) SET UP but do not evaluate the integral in spherical coordinates (dp do do) that gives the volume of E. Indicate how you found the limits of integration for p, , and 0. a)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 63E
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