Math 233. Test: Form M, April 25, 2014
Name:
Instructions. Do each of the following 7 problems. Please show all appropriate work in order
to receive maximal credit. You may use a scientic nongraphing calculator.
1. (10 pts) Let f (x, y) =
(a) Evaluate
lim
Math 233, Test 1, Spring EDDIE-
Nalne: [At-1"] JJ-xf'g T'III'I 'qu RIB.
Instructions. Do the rst queetiouL and any seven of the Inst. eight questions. Please do
your been e.an Show all appropriate work. Thank you.
1. (14 lots] {3.) W'rite the formu
Math 233, Test 3, Spring 2007 Name: Instructions. Do the first question, and any four of the last five questions. Please do your best, and show all appropriate work. Thank you. 1. (18 pts) (a) Compute the divergence of the vector field F(x, y, z) = -yi +
Math 233: Test II, Spring 2006 Multiple Integrals Name: Instructions. Do question 1 and any 4 of questions 2 through 6. Please justify all answers.
3 2x
1. (15 pts) (a) Sketch the region of integration for
0 0
f (x, y) dy dx.
(b) What is the value of inte
Math 233, Test 1, Spring 2005 Name: Hints and Answers Instructions. Do the rst question, and any seven of the last eight questions. Please do your best, and show all appropriate work. Thank you. 1. (14 pts) (a) Describe the level surface for f (x, y, z) =
Math 233, Test 1, Spring 2006 Name: Instructions. Do the first question, and any seven of the last eight questions. Please do your best, and show all appropriate work. Thank you. 1. (14 pts) (a) Write the formula used to calculate implicitly defined by F
Math 233, 'Iest 3, Spring 211136
. _I'
Name: I 3 3 WI? Ff
Instructions. Do the rst question, and anyr four of the last ve questions. Please do your
best, and show all appropriate work. Thank you.
1. (18 pts] {a} Write the formula for the]? where F{£,y,z
Math 233: Test 11, Spring 2006 -- Multiple Integrals
Name:
Instructions. De qnestien 1 and any 4 ei' queetiens 2 thrcugh 6. Flees-e justin all enswem.
H 2.x
1. (15 {its} {e} Sketch the region cf integration fer f f u yMy nix.
' ' e D
t r3, e
[b]
Math 233, Test 1, Spring 2004 Name: Instructions. Do the first question, and any seven of the last eight questions. Please do you best, and show all appropriate work. Thank you. 1. (14 pts) (a) Describe the level curve for f (x, y) = x2 + y 2 - 4 at level
Math 233, Test 1, Spring 2004 Name: Hints and Answers
Instructions. Do the rst question, and any seven of the last eight questions. Please do you best, and show all appropriate work. Thank you. 1. (14 pts) (a) Describe the level curve for f (x, y) = x2 +
Math 233: Test III, Spring 2004 Line Integrals and Vector Fields Name: Instructions: Complete any ve of the following six problems. Please show all of your work.
1. (a) (5 pts) Sketch several representative vectors of the vector eld F(x, y) = xi + yj.
(b)
Math 233, Test 1, Spring 2005 Name: Instructions. Do the rst question, and any seven of the last eight questions. Please do your best, and show all appropriate work. Thank you. 1. (14 pts) (a) Describe the level surface for f (x, y, z) = x2 + y 2 + z 2 +
Math 233: Test III, Spring 2005 Vector Fields & Line Integrals Name: Instructions. Do question 1 and any four of questions 2 through 6. Please justify all answers. 1. (a) (2 pts) Define what is meant by a conservative vector field F. (b) (3 pts) Given a v
Math 233: Test II, Spring 2004 Multiple Integrals Name: Instructions: Complete each of the following problems.
2 y
1. (15 pts) (a) Evaluate the iterated integral
0 0
2xy dx dy.
(b) Write the formulas for Mx , My , x, y when nding the center of mass of a p
Math 233, Test 3, Spring 2005 Name: Hints and Answers f = F.
1. (a) The vector eld F is conservative if there is a function f such that (b) divF = curlF = M (x, y, z) + N (x, y, z) + P (x, y, z). x y z i+ M P z x j+ N M x y k
P N y z
(c) If the line integ
Math 233, Test 1, Spring 2007
Name:
Hints and Answers
Instructions. Do the rst 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 dierentiable fun
Math 233, Test 3, Spring 2007 Name: Instructions. Do the rst question, and any four of the last ve questions. Please do your best, and show all appropriate work. Thank you. 1. (18 pts) (a) Compute the divergence of the vector eld F(x, y, z) = yi + xj + ez
Math 233. Test: Form M, April 25, 2014
Name:
Instructions. Do each of the following 7 problems. Please show all appropriate work in order
to receive maximal credit. You may use a scientic nongraphing calculator.
1. (10 pts) Let f (x, y) =
(a) Evaluate
lim
Math 233: Test II, Spring 2014
Name:
Instructions. Do each of the following ve questions. Please justify all answers and show all
appropriate work; you may use a scientic non graphing calculator.
3
18x2
1 dy dx represents the area of a planar region R.
1.
Math 233.
Week 1: Written Homework
Due: Thursday April 10
Instructions. Do each of the following ve problems. Show all appropriate details in your
solutions.
1. For each equation, indicate the choice that best describes its level curves.
3.
z = 5x2 + 8y 2
Math 233.
Week 2: Written Homework
Due: Thursday April 17
Instructions. Do each of the following ve problems. Show all appropriate details in your
solutions.
1. Use the denition of dierentiability to show that the function given by
f (x, y) = 3x2 2xy
is d
Math 233.
Week 3: Written Homework
Due: Thursday April 24
Instructions. Do ve of the following six problems. Show all appropriate details in your
solutions. Please write answers on a separate sheet so you have room to show all work.
1. Consider the surfac
Math 233.
Week 2: Written Homework
Due: Thursday April 17
Instructions. Do each of the following ve problems. Show all appropriate details in your
solutions.
1. Use the denition of dierentiability to show that the function given by
f (x, y) = 3x2 2xy
is d
Math 233, Review Questions for Test 1 over Chapter 12 Name: 1. Sketch level curves for the following functions at levels c = 4, 0, 4. (a) f (x) = x2 + y 2 (b) g(x) = x + y 2. Sketch level surfaces for the following functions at the specied levels for c. (
Math 233.
Week 3: Written Homework
Due: Thursday April 24
Instructions. Do ve of the following six problems. Show all appropriate details in your
solutions. Please write answers on a separate sheet so you have room to show all work.
1. Consider the surfac
Math 233, Review for Test 2 The test will cover chapter on multiple integrals. The key topics are as follows. Evaluating iterated integrals. Setting-up and evaluating multiple integrals for area, volume, mass, center of mass in rectangular, cylindrical or
Math 233: Test II, Spring 2014
Name:
Instructions. Do each of the following ve questions. Please justify all answers and show all
appropriate work; you may use a scientic non graphing calculator.
3
18x2
1 dy dx represents the area of a planar region R.
1.
Math 233.
Week 1: Written Homework
Due: Thursday April 10
Instructions. Do each of the following ve problems. Show all appropriate details in your
solutions.
1. For each equation, indicate the choice that best describes its level curves.
z = 5x2 + 8y 2
8
Math 233: Test II, Spring 2007 Multiple Integrals Name: Instructions. Do question 1 and any 4 of questions 2 through 6. Please justify all answers and do not use a calculator.
3 9x2
1. (15 pts) (a) Sketch the region of integration for
3 0
y dy dx.
Answer.
Math 233: Test II, Spring 2007 Multiple Integrals Name: Instructions. Do question 1 and any 4 of questions 2 through 6. Please justify all answers and do not use a calculator.
3 9x2
1. (15 pts) (a) Sketch the region of integration for
3 0
y dy dx.
3
9x2
(