{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw3 - x 2 y 2 ≤ z 2 with z ≥ 0 and below the plane z =...

This preview shows page 1. Sign up to view the full content.

32B Killip Homework 3 Due Friday Apr 23 (1) From Section 16.6: 6, 12, 34, 38. (In 5th Ed, Section 16.7: 6, 10, 32, 36.) (2) Section 16.7: 20 (5th Ed: Problem 10 in Section 16.8.) (3) Section 16.8: 20 and 26 (5th Ed: Problems 6 and 22 in Section 16.8.) (4) Let T be the torus given in spherical polar coordinates by the equation ρ sin φ . (a) Draw the intersection of the torus with the plane y = 0. (I want a two dimensional sketch on axes marked ‘ x ’ and ‘ z ’.) (b) Calculate the volume of the torus. (5) Consider the region inside the cone
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x 2 + y 2 ≤ z 2 with z ≥ 0 and below the plane z = 1-1 2 y . (a) Write the integral of f ( x,y,z ) over this region in spherical coordinates. (b) Repeat part (a) with cylindrical coordinates. (6) Compute the location of the center of mass of half of a solid sphere. Note: The ﬁrst mid-term covers the material up to and including “Triple Integrals in Spherical Coordinates”. See http://www.math.ucla.edu/~killip/32b/ for the order of topics. 1...
View Full Document

{[ snackBarMessage ]}