Prelim 3 Sp'06

# Prelim 3 Sp'06 - Math 192 Prelim 3 Calculators are not...

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

Math 192 Prelim 3, April 27, 2006 Calculators are not allowed. Write your section number and TA’s name on the front of your workbook. This exam is worth 100 points. Point values for each problem are in parentheses. Show all your work . 1. (15) For each of the following, set up an integral using the indicated coordinates to find the volume but do not evaluate the integral. i) Cylindrical coordinates: The region that lies inside the sphere x 2 + y 2 + z 2 = 2 and outside the cylinder x 2 + y 2 = 1. ii) Spherical coordinates: The region enclosed by the cone z = x 2 + y 2 between the planes z = 1 and z = 2 . . 2. (15) Find the mass of a wire that lies along the curve r ( t ) = ( t 2 - 1) j + 2 tk, 0 t 1, if the density at any point on the curve is given by δ = 3 t/ 2. 3. (15) Find the flow of the vector field F ( x, y, z ) = 6 zi + y 2 j + 12 xk along the curve C given by r ( t ) = (sin t ) i + (cos t ) j + ( t/ 6) k, 0 t π
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern