MIT OpenCourseWare http ocw mit edu 18 02 Multivariable Calculus Fall 2007 For information about citing these materials or our Terms of Use visit http ocw mit edu terms 18 02 Problem Set 10 Due Thursday 11 15 07 12 45 pm 10 points Part A Hand in the underlined problems only the others are for more practice Lecture 27 Thu Nov 8 Exam 3 covering lectures 18 26 Lecture 28 Fri Nov 9 Triple integrals in rectangular and cylindrical coordinates Read 12 8 to p 841 Notes I 3 14 6 esp Examples 1 2 3 14 7 pp 988 989 Work 12 8 5 23 14 6 41 14 7 9 19 5A 1 2abcd 3 4 5 6 7 Lecture 29 Tue Nov 13 Spherical coordinates Gravitational attraction Read Notes I 4 CV 4 G 14 7 pp 990 992 Work 12 8 9 11 15 27 55 5B 1abc 2 3 4abc 5C 2 3 4 16 points Part B Directions Attempt to solve each part of each problem yourself If you collaborate solutions must be written up independently It is illegal to consult materials from previous semesters With each problem is the day it can be done Write the names of all the people you consulted or with whom you collaborated and the resources you used Problem 1 immediately 4 points x y Find the ux of the vector eld F 2 2 outwards through any circle centered at r r 1 0 of radius a 1 Consider the cases a 1 and a 1 separately Explain your answers with diagrams Optional use the applet on the course web page to get a better understanding of what happens when a changes from a value lower than 1 to a value greater than 1 Problem 2 Friday 4 points Do 14 6 39 Suggestion use the order dx dy dz The numerical answer is in the back of the text Feel free to check your work using it Problem 3 Tuesday 4 points The average value of f x y z over a region D in space is 1 f x y z dV V D volume of D V D D Set up the integral both in cylindrical and spherical coordinates for the average distance from a point in the solid sphere of radius a to a point on the surface and evaluate both integrals Put the point on the surface at the origin and make it the South Pole of the sphere Problem 4 Tuesday 4 points Notes 5C 5 1
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