Math 233, Test 1, Spring 2008 Name: Hints and Answers
Instructions. Do the first question, and any six of the last seven questions. Please do your best, and show all appropriate work. Thank you. F 1. (14 pts) (a) Write a formula for for the differentiable
Math 233: Test II, Spring 2008 Multiple Integrals Name: Hints and Answers
Instructions. Do question 1 and any four of questions 2 through 6. Please justify all answers and do not use a calculator.
0 y+4
1. (10 pts) (a) Sketch the region of integration for
Review Questions for Test 3 Hints and Answers A. Some Review Questions on Vector Fields and Operations. A1. (a) The sketch is left to the reader, but the vector eld appears to swirl in a clockwise direction, and the arrows get longer farther away from the
Math 233, Review for Final Test Hints and Answers
2 2 0 2 2
1. (a) M =
S
x2 zdS =
0
r5 cos2 1 + 4r2 dr d. (2r3 cos 1)r dr d = 4.
(b) Flux =
S
(F N)dS =
0 0
2. First curlF = 3i j 2k and NdS = ( 2 i + 1 j + k)dA and so 3 3 F dr =
C S
(curlF) NdS =
R
13 13
Math 233, Test 1, Spring 2008 Name: Instructions. Do the first question, and any six of the last seven questions. Please do your best, and show all appropriate work. Thank you. F 1. (14 pts) (a) Write a formula for for the differentiable function F (x, y)