Test3Old

# Test3Old - (c(10 points Evaluate I = ZZ R p x 2-2 xy 5 y 2...

This preview shows pages 1–6. Sign up to view the full content.

MATH 231, Calculus III, Section 1, Fall 2007 Test 3 Date: Nov. 14, Wednesday Time: 10:00 am - 10:50 am Please write clearly, reduce answers to their simplest form, and box your answers. To receive full credit you must show ALL your work. Student's Name (Please print): __________________________________________ Pledge: On my honor as a student at the University of Virginia I have neither given nor received aid on this test. Signature: _______________________________ Problem Points Score 1 25 2 25 3 25 4 15 5 10 6 (Bonus) 10 Total 110/100

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

View Full Document
Problem 1 (25 points) Find the volume of the region E bounded above by x 2 + y 2 + z 2 = 2 and below by z = x 2 + y 2 . 1
Problem 2 (25 points) Consider the region R in R 2 bounded by x 2 - 2 xy + 5 y 2 = 1, and the transformation T given by x = u + v 2 , y = v 2 . (a) (10 points) Find, describe and sketch the region S in the uv -plane corresponding to R (via the transformation T in the sense that T : S R ). (b) (5 points) Find the Jacobian of T (Use the proper notation!).

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

View Full Document

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.

Unformatted text preview: (c) (10 points) Evaluate I = ZZ R p x 2-2 xy + 5 y 2 dA using the transformation T . 2 Problem 3 (25 points) Find the work done by the force ﬁeld F ( x,y ) = 3 x 2 i + (4 x + y 2 ) j on a particle that moves along the following paths: (a) (10 points) C 1 is the line segment from (1 , 0) to (0 , 1). (b) (15 points) C 2 is part of the curve x 2 + y 2 = 1 for which x ≥ 0 and y ≥ 0 (the particle moves counterclockwise). 3 Problem 4 (15 points) Find the mass of a ball given by x 2 + y 2 + z 2 ≤ 9 if the density at any point, denoted by D ( x,y,z ), is proportional to its distance from the origin. Problem 5 (10 points) Using cylindrical coordinates set up, but do not evaluate the integral I = ZZZ E dV, where E is the region bounded above by x 2 + y 2 + z 2 = 4 and below by z = √ 2. 4 Bonus Problem 6 (10 points) Solve Problem 5 using spherical coordinates. 5...
View Full Document

## This note was uploaded on 04/24/2009 for the course CALC 2401 taught by Professor Stojanovic during the Spring '09 term at Georgia Tech.

### Page1 / 6

Test3Old - (c(10 points Evaluate I = ZZ R p x 2-2 xy 5 y 2...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online