2313-practice-mid4

# 2313-practice-mid4 - MAC 2313 Fall 2010 Midterm 4 Review...

This preview shows pages 1–2. Sign up to view the full content.

MAC 2313, Fall 2010 — Midterm 4 Review Problems 1 We will discuss these problems in class on Monday 11/15. Solutions will be posted on the course webpage over the weekend. 1 A bounded region in the first octant of 3-dimensional Euclidean space has the surface x + y + z 2 = 1 as part of its boundary. The remainder of its boundary is given by portions of the places x = 0, y = 0, and z = 0. Compute the triple integral of z over this region in space. (You should probably begin by sketching this region.) 2 Let R denote the portion of the unit ball { ( x, y, z ) : x 2 + y 2 + z 2 1 } that lies inside the solid cone { ( x, y, z ) : z radicalbig x 2 + y 2 } . Compute the volume of R with triple integrals in both cylindrical and spherical coordinates. 3 Let R denote the portion of the unit ball { ( x, y, z ) : x 2 + y 2 + z 2 1 } that lies inside the prism { ( x, y, z ) : x 0, y 0, and x + y 1 } . Set up a triple integral to compute the volume of R . 4 Find the work done by the field F = y i x j + k as a particle is moved from (1 , 0 , 0) to (1 , 0 , 1) along the path r ( t ) = ( cos t, sin

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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