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Unformatted text preview: SI: Math 122 Test 2 October 14, 2008 N amexﬁ’—_ Style Points — Directions: 1. No books, notes or annoying political ads about Issue 6. You may
usa a calculator to do routine arithmetic computations. You may not
use your calculator to store notes or formulas. You may not share a
calculator with anyone. . You should show your work, and explain how you arrived at your an— swers. A correct answer with no work shown (except on problems
which are completely trivial) will receive no credit. If you are not sure
whether you have written enough, please ask. . You may not make more than one attempt at a problem. If you make several attempts, you must indicate which one you want counted, or
you will be penalized. On this test, explanations count. If I can’t follow What you are doing,
you will not get much credit. . You may leave as soon as you are ﬁnished, but once you leave the exam, you may not malts any changes to your exam. l. (10 points) For the differential equation 2. (15 points) Solve the following differential equations. (a)d’£l=my+ﬂ = X+ i
BE 33 < 07
l
——d :Sx _‘_._d><
SH 7 + x
2
Q/hy : §+d2mx+c
e E7—
\{ = CXE
(13) md; —3y2 m1 y(1) = 5 3
YI~EV=><3 “’02—? q‘cm=x
7K C J‘édx ?>_9nn¥
Px3:€ :e __—_
*3 A
1: —L::3 jX‘ X3 CIK +a=7<gix4ra
X
5“ '3
B=l+c c=4 v=><+“‘x
(0) 2y”+2y’+y=0
aRl+aQ+\'=O
.. + _ 1r. ' ~
R_ a‘W—‘8 : ; 3““=—\:t_1.
; 1
cQ=—1 [3:
—><.
\[ = e C‘ cosx + Q;S\NX 3. (15 points) Alex Cooke is making cookies! YES! To make the mix, he
uses a large tank (about the size of Charles) and ﬁlls it up with 100
gallons of hot sauce that contains 10 pounds of berries and cream. He
pumps in 5 gallons of hot sauce per minute, with 2 pounds of berries
and cream per gallon, and he drains the tanl: at the same rate. (a) Write a diﬂerential equation, with initial condition1 for the amount
of berries and cream in the tank. ((3) Alex’s mix Will be ready when there are 15 lbs of berries and cream
in the tank. At what time will that happen? _,I
let IOO ~———d6=R\*Ro: [0‘53
‘0 d4; IOO
QE+L =\o 8Coj=l0
cit 3°
(b) Solve the differential equation from part( S albeit a?) t
_ __1_ = (1:3 = Q. = e __ 20 l0 iv
l 3,5": —%'t é°b* CT}
= Li: d'b'l‘c :8 EDGE
e” ‘
_,Lt:. — qqo
_ goo+9399 to =9~°O+Q C‘
__L':
3Q 4. (10 points) Match each of the following polar equations with the correct ' equation in rectangular coordinates.
......___3 7‘2 cos 26 = 9 7": 60056
0t _ 1 71— 30059+33m9 T2 sin 29 = 9 3’,
H
10
+
rs
CE

DD
U
[Q
i I
CC b) 2273/ = 9 f) (zm3)2+y2=9 4. (10 points) Match each of the following polar equations with the correet equation in rectangular coordinates. i“ 7‘2 cos 29 = 9 T = ﬁnest? C 1 T: 3cos9+351119 £4...— 7‘2 Sin29 = 9 e) (:3—3)2+y2=9 4. (10 points) Match each of the following polar equations with the correct
equation in rectangulai~ coordinates. L cl 7‘2 cos 26 = 9 T=6cosﬂ 7‘: l
3cos§+35in§ rgsmzamg d) 3:2—y‘:
e) (m—3)g+y2=9
f):1:2+y2= 4. (10 points) Match each of the following polar equations with the correct
equation in rectangular coordinates. Ox. r2 cos 26 = 9 =6c050 7‘: 1 .
30059+35m9 7'2 Sin 29 = 9 '3 a.) $2+y‘= 5. (10 Points) (3.) Set—up an integral to ﬁnd the area Of one petal of the 4 leaf rose
7‘ = 3 cos 26
Do not solve the integral. 2'“— A'; 1 (3Cosa632
“k. T“ 0‘6 (b) Setup an integral to ﬁnd the the area inside T = sin 9 and outside
7‘ = l + cos 6.
Do not solve the integral. T "W
2
A : (Sm 6) d9 _f(1+¢03€jde
El 1
1% ~35
0R 1T 1‘ __ 3 (Hcosefde
8 2L 'EE ’9. 6. (15 points) Consider the parametric curve given by
33:5th y=2c03t (3) Sketch the graph for 0 S t 5 27r and iﬁdjcate the direction of
increasing t. w)Fmdgg
d Q1 JG
\! : OH: = —'Q,S\N __'D‘__‘_RN_b
dK g§_ C06t
E
(c)Fmd%
d ‘iil .Q“XE "X
dzv _ a“; om __ db “1””:
dXL dx d\x
dJc OVC '2.
__ c, '5
ﬂ. 3:: t as";ch Cagt 7. (10 points) Find the arc length of the curve I1
=§ LH t 0“:
E
35.11
2(“‘*9\ z E (ebb951)
3 ‘3 3 *‘H
1 3—. (737’ : —
3 3 3 8. (10 points) Find the area of the region between the :v—axis and the curve m=2cott ym2sin2t f0r0<t<7r.
O 'z
A c—S aemz—t 1C$C JG (5“:
O o
__ .3 .— qt\ : _—_ SH c3)“ 1T TY ...
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This note was uploaded on 02/17/2010 for the course MATH 122 taught by Professor Butler during the Spring '07 term at Case Western.
 Spring '07
 Butler

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