Northwestern University
NetID:
Math 230 Final Exam
Spring Quarter 2010
June 8, 2010
(2 points) Put a check mark next to your instructors name and section:
Heller
Herzig
9:00
11:00
Points Score
possible
0
2
1
10
2
10
3
10
4
13
5
12
6
12
7
14
8
20
9
14
10
1
Name:
Northwestern University
Id #:
Math 230 Exam 1
Spring Quarter 2011
April 20, 2011
Put a check mark next to your instructors name and section:
Walker
Khorami
Burslem
9:00
11:00
1:00
Walker
10:00
Khorami 12:00
Bode
2:00
Instructions:
Prob.
Points Score
Northwestern University
NetID:
ID # :
Math 230 Final Exam Solutions!
Fall Quarter 2012
Wednesday, December 12, 2012
Complete the front page! Mark your section! [3 points!]
Do not write your name on this exam!
Write your NetID and your Student ID Number in
Northwestern University
NetID:
ID # :
Math 230 Test #1 Solutions!
Fall Quarter 2012
Wednesday, October 24, 2012
Complete the front page! [1 point!]
Instructions:
Show ALL of your work on the pages provided! Explain your reasoning using
complete sentences
Northwestern University
NetID:
ID # :
Math 230 Test #2 Solutions!
Fall Quarter 2012
Monday, November 19, 2012
Complete the front page!
Do not write your name on this exam!
Write your NetID and your Student ID Number in the spaces provided at
the top of th
Northwestern University
NetID:
Math 230 Final Exam
Spring Quarter 2011
June 7, 2011
(2 points) Put a check mark next to your instructors name and section:
Walker
Khorami
Burslem
9:00
11:00
1:00
Points Score
possible
0
2
1
14
2
6
3
10
4
15
5
9
6
22
7
14
8
NetID:
Northwestern University
ID # :
Math 230 Final Exam
Spring Quarter 2012
Tuesday, June 5, 2012
Instructions:
Show ALL of your work on the pages provided! Explain your reasoning using
complete sentences and correct grammar, spelling, and punctuation.
NetID:
Northwestern University
ID # :
Math 230 Final Exam Solutions
Winter Quarter 2012
Monday, March 12, 2012
Instructions:
Show ALL of your work on the pages provided! Explain your reasoning using
complete sentences and correct grammar, spelling, and pu
NetID:
Northwestern University
ID # :
Math 230 Final Exam
Winter Quarter 2012
Monday, March 12, 2012
Instructions:
Show ALL of your work on the pages provided! Explain your reasoning using
complete sentences and correct grammar, spelling, and punctuation.
Id #:
Northwestern University
NetID:
Math 230 Exam 1
Spring Quarter 2010
April 27, 2010
Put a check mark next to your instructors name and section:
Heller
Herzig
Prob.
9:00
11:00
Points Score
possible
1
24
2
12
3
14
4
8
5
10
6
5
7
6
8
6
9
15
TOTAL
100
Wal
Northwestern University
NetID:
ID # :
Math 230 Test #1
Fall Quarter 2011
Put a check mark next to your instructors name and section:
Treumann
8:00
Treumann
9:00
Rozenblyum
9:00
Khorami
10:00
Broderick
10:00
Bohmann
11:00
Li
11:00
Broderick
12:00
Li
12:00
Answers to practice problems on gradients, optimization and Lagrange multipliers.
Gradients, directional derivatives and extrema for functions of several variables:
1. Suppose that f (x, y ) = x3 3x + y 2 6y
Answers to practice problems on gradients, opti
Question 1 (2 poilts). D'Carter. a biologist, is tracking a Polar Bear arourcl thc Alctic Circle. Sirrce
is a Polal Bcar'. it'nvallis aklrg a path dcscribed lrv the 1;olar ecluation rsin(d)tarr(01 : 1. D'Clarter
it
pl'efcrs Clart'csi:ur coorclirt:rtes. so
joh^
6<evr,u",t;',w
o;f:nfra"
Math 230 Test 2 Review Worksheet
Question L. TYiangle Being is on its favorite ride, the MerryGoRound, and is thus travelling &round
the circle x2 + y2 :4.
(a) Find the eurvature of this eircle. Show your
tdct) c
!l f
*t"
'
a1t!4
)otn^ J gcfw_y dr
Math
23A Worksheet #L
JanuarSr 12,2012
NetrD: i. i Lll t
Partner(s): nna: *l ll
,
"rsfl
?E3
'You may work with a partner on this workgheet, but you must write you osrn solutions
to the problems and write the NetID of your collabora
) uh* ) r, v *ro1au
Math 230 Worksheet #2
January 19,2012
Partner(s1,
NetID:
nrP
cfw_tr3
a partner on this worksheet, but 1lou rnust write you own solutions
to the problems and write the NetID of your collaborator on your worksheet. Turn in your worksheet
>hn
Math 230 Wbrksheet #3
January 26,2012
p.
l ".
*.1
o
,AnLC\.dA
,j') 5"i
q
1 l(
itck
, .c
e
'11
v\^
,
You may work with a partner on this worksheet, but you must write you own solutions
to the problems and write the NetID of your collaborator on your wo
SI^ Te.vMt)M
Math 230 Worksheet #4
February 9,2012
Partner(s):
,^.aS
ni
cfw_l
Instructions: You may work with a partner on this worksheet, but you must write you own col.utions
to the problems and write the NetID of your collaborator on yolr worksheet. T
A.[r^ T.v'*,"; r' vr,
Math 230 Worksheet #5
February 16,2012
NIs11p;
partner(s):
ir;tcfw_51
tJ"
6aa5 9f
I
+
tz c
67,1
rnstructions: You mav work with a partner on this worksheet, but you must write you own solutions
to the problems and write the NetID of
ltf^
Jueu*r"*.\*^
Math 230 Worksheet #6
March 1.20L2
NetID: ir;'cfw_5
!v
Partner(s)t
3
n^r"i
*i
[!

*si*
YS 4
Instructions: You may work with a partner on this worksheet, but you rnust write you own solutionS
to the problems and write the NetID of you
Question 1 (2 points). Let,4 be the poilt A: (I,1,4), ancl let B be the poirrt B
all values of c such that the point P  (2,i,c) is closer to,4 tlian to B.
.i
itD
i:!

(3.2,3). Find
!(
rl
ri
.
i'
L.
\i,) I
ll
I
1,
,
y"dt
t
Question 3. Jack and Jill ar
Practice problems on gradients, optimization and Lagrange multipliers.
Gradients, directional gradients, optimization functions of several variPractice problems on derivatives and extrema for and Lagrange multipliers.
ables:
Gradients, Suppose that f (x,