Math 234 Practice Second Midterm #2 Solutions
Winter 2016
1. Find the area of the part of the cylinder x 2 Cz 2 Da2 that lies within the cylinder r 2 Dx 2 Cy 2 Da2 .
Solution: To compute the surface area we need dS . Two possibilities are either
r
q
1
dS
Math 234-0
Midterm 2
Multiple Integration and Vector Calculus
Prof. Brockmann
Name:
Section 57/67
March 3rd, 2011
TA:
Rules:
Permitted equipment during this midterm are: brain, pencil or pen, eraser, blank paper
and a drink.
This implies that electronic
Math 234
Second Midterm
Last name:
NetID:
First name:
Instructions
This examination consists of 5 questions for a total of 100 points.
You have one hour to complete this examination.
Do not use books, notes, calculators, computers, tablets or phones.
Math 234 Final Exam
Fall Quarter 2014
December 10, 2014
Last name:
Email address:
First name:
NetID:
Instructions
This examination consists of ? questions for a total of ? points.
You have two hours to complete this examination.
Do not use books, notes
Math 234 Practice Second Midterm #1 Solutions
Winter 2016
1. Find the area of the sphere x 2 Cy 2 Cz 2 D a2 that is outside the cylinders x 2 Cy 2 ax D 0 and
x 2 Cy 2 Cax D 0.
Solution:
One way to do this is to find the surface area inside the cylinders a
Math 234 Final Exam
Fall Quarter 2014
December 10, 2014
Last name:
Email address:
First name:
NetID:
Instructions
This examination consists of 10 questions for a total of 100 points.
You have two hours to complete this examination.
Do not use books, no
Question 2 (30 points). Let F(a:, y, z) = sin yi + (:17 cos y + cos z)j y sin z k.
1. Compute the curl of F.
->
_._3 5 T7 '7!
V X? = L J k
.32. A 3.
3x 63 3%
3&3 V. 0on was - gggd
1 K -Swa<$L~$\, ~o, 00330033)
_-5
O
2. Compute the line integral of F along
Northwestern University
Math 234 Section 51
Second Midterm
Winter Quarter
February 28
Last name: _ NetID:
First name:
Instructions
0 This examination consists of 5 questions for a total of 100 points.
0 You have one hour to complete this examination.
0 Do
NetID:
Northwestern University Id #_
Math 234-0 Final Exam
Spring Quarter 2013
Tuesday, June 11, 2013
Instruct ions:
0 Mark your section.
0 Read each problem carefully.
0 Write legibly.
a Show all of your work on these sheets.
0 The exam consists of 10
Math 234 Midterm #1
Spring 2016
Class time:
Name:
Instructions:
1. Print your name on this page in the space provided.
2. Show all work. For partial credit we must be able to follow your logic.
Neatness counts. We also need to be able to read what you wri
Math 234 Practice Second Midterm #2
Winter 2016
Name:
Class time:
Instructions:
1. Print your name and class time on this page in the space provided.
2. Show and explain all work. Please describe in words (even a few) what you are doing.
Partial credit wi
Math 234-0
Multiple Integration and Vector Calculus
Essentials Midterm 2
Section 57/67
Prof. Brockmann
Fields
You need to be familiar with the concepts
Scalar field (r)
Vector field F(r)
the nabla operator = ix + jy + kz
gradient of a scalar field (th
Math 234-0
Multiple Integration and Vector Calculus
Midterm 2
Prof. Brockmann
Section 47
Mar. 5th, 2009
Name:
1. Determine which of the vector fields below are conservative and if so compute their potential.
a) F = 3x2 + 2y 2 i + 4xy + 6y 2 j
b) F = y i z
Math 234 Midterm #1
Spring 2016
Class time:
Name:
Instructions:
1. Print your name on this page in the space provided.
2. Show all work. For partial credit we must be able to follow your logic.
Neatness counts. We also need to be able to read what you wri
Math 234 Midterm #2
Spring 2016
Name:
Class time:
Instructions:
1. Print your name on this page in the space provided.
2. Show all work. For partial credit we must be able to follow your logic.
Neatness counts. We also need to be able to read what you wri
Math 234
NAME
FINAL EXAM
I.D. #
Winter Quarter 2006
Instructions:
Instructor: Prof. Gui-Qiang Chen
Write your name and I.D. number above. Show all work on
these pages, and make sure that your final answer is clearly
shown. No books and calculators are per
Northwestern University
Name:
Math 234 Final Exam
Summer 2012
Thursday, August 9, 2012
Instructions:
Read each problem carefully.
Write legibly.
Show all of your work on these sheets. Points may be lost for incomplete work.
The exam consists of 10 pro
01406E5 3-63B9-4239-AElB-1 12ABTCC81EE
NU Math 234 SP 15 Final Exam
#1 2 of 12
Problem 1 (21 points, 3 points each) True or False. Circle the correct answer clearly.
1 x2 1
T a/f x+2ddx=ff x+2dxd
( > 0 0 y y 0 0 y y
F (b) An annulus in R2, such as 1 S
Math 234 Practice Second Midterm #1
Winter 2016
Name:
Instructions:
1. Print your name on this page in the space provided.
2. Show and explain all work. Please give some explanation of what you are doing. Partial
credit will be given only for written work
Math 234 Midterm Exam Summer 2012 Page 2 of 8
1. (20 points) A lamina. occupies the region in the 151; quadrant bounded by the line y = x,
the y- axis and the circles 5112+ y2 = 4 and $2 + y2 = 9. Its density function is p(;t:, y) =
earcmnW/r). Find its m
Math 234-0
Midterm 2
Multiple Integration and Vector Calculus
Prof. Brockmann
Section 57/67
March 3rd, 2011
Name:
TA:
Rules:
Permitted equipment during this midterm are: brain, pencil or pen, eraser, blank paper
and a drink.
This implies that electronic
Math 234-0
Midterm 2
Multiple Integration and Vector Calculus
Prof. Brockmann
Section 47
Mar. 5th, 2009
Name:
1. Determine which
of the vector2 fields below are conservative and if so compute their potential: (a)
2
2
F = 3x + 2y i + 4xy + 6y j (b) F = y
MATH 2340 Multiple Integration and Vector Calculus
Winter 2010, Section 77, Midterm Exam 1, February 4, 2010
Name: SD Lia.
Instructions:
1. Print your name on each page.
2. Show all your work for full credit.
3. Cross out anything you dont want graded.
4.
Math 234 Test 2
Fall Quarter 2014
November 17, 2014
9 l
Your instructor: Xia (11:00am) Getzler (1:00pm)
Your Name
Instructions:
0 Read each problem carefully.
9 Write legibly.
a Show all your work on these sheets.
0 Make sure that your nal answer is clear
Math 234 Midterm #2 Solutions
Winter 2010
1. Find the surface area of the part of the paraboloid z = 16x 2 y 2 = 16r 2 that lies above the
x y -plane.
Solution:
The simplest way to do this is to parameterize using r and in the plane z = 0; one then gets
a
Math 234 Test 2
Fall Quarter 2014
November 17, 2014
Your Name
Your instructor:
Xia (11:00am)
Getzler (1:00pm)
Instructions:
Read each problem carefully.
Write legibly.
Show all your work on these sheets.
Make sure that your final answer is clearly ind