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Unformatted text preview: Math 122 Test 2 October 17, 2006 Name K E Kr .. Cir‘i UT 943 00 [\D H 00% Style Points ._____.____._______J__________.._ Total Directions: 1. No books, notes or opinions (this is not a SAGES class). You may
use 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. 2. 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. 3. 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. 4. On this test, explanations count. If I can’t follow what you are doing,
you will not get much credit. 5. You may leave as soon as you are ﬁnished, but once you leave the exam,
you may not make any changes to your exam. 1. (10 points) (a) For the diﬁerential ecuation 2 17(3), y), Where F($,y) is given below:
a; O 1 2 3 4 O 10 —l —1 O 1 E O 1 O 1 O y 2 u] 0 —1 1 1 3 —1 1 0 1 0 4 1 1 —1 —1 1 9(4) 2. (15 points) Find the solution for the following differential equations. (a) e“m2%=a§y2+m
x2.
8 l... Ch, zfxe aha
\DZM
x1
ﬂammgbr 3. ~+C,.
“3..
X2
: TR g... C
\I N w}. “* 5
(b) (1+m)%+y:cosac, y(0)=1
’ l Coax l
\{ ‘+ My , POO: ——
\1—X ‘Lr‘r’x /+>(
QCX‘) “ C0500
S...de Hx M
Hx .QVEh4x)
P66) : e :7 E3 t: \‘rX 3. (15 points) A tank initially contains 60 gallons of pure water. Brine
containing 1 lb of salt per gallon enters the the tank at 2 gal per minute
and the mixed solution leaves the tank a 3 gal per minute. (a) Write a differential equation for the amount of salt in the tank
(With initial condition). Q
«:1 i ( 
3.: a. 2” l m 3 ‘7’ 0‘) "" O
\:L dE; 2“ Q” (90 “t
0W 3
+—~7=D~ 0;): i. QLJc) 3Q
we a 6 6° W
(b) Solve the differential equation from part ( '3
:7 O—t) '3
.L. (Go63
Becca \i _ (63c: wt) "‘ (C) How much salt Will. the tank contain after 20 minutes? 4. (10 points) Match each of the following differential equations with the correct solution. C y”+2y’+y=0 y”+3y’+2y=0 y"+6y'+13y = 0 y”+4y=0 y”~7y’+10y: 0 a) y = (318% + 0265“ b) y =2 6—39: [cl cos 233 + Cg sin 22:] c) y a ole—m + c2368”: d) y = ale—m + 026‘ ‘ e) y = 01 cos 22: + 02811123: f) none of these 5. (10 points) (a) Which of the following is not a polar repressentation for the point (—2., 2).
8» Mfr—El b> [miiii
d) [2J2 e) None of these (b) Find an equation in rectangular coordinates for the curve Whose
equation in polar coordinates is 7" 2 ~4c1036+381116 Z P .—= ——’—\\(‘Co‘>€>‘*’7’rgwe Xl+\f’2 .__ ..I—n< +37 6. (10 Points)
(a) Find the points of intersection (ray) of 7’22 and r=1+20086 “I Cl:
9 3) 3 X=aCosC¥g>ri x: gzcg5(_1;‘):i
V:25w(§] :@ \/== 26mg?) 25
(a???) Off/:23 (b) Set up an integral to ﬁnd the area of the region that lies inside
the 1i1na§0n 'r' :2 1 + 2 cos 6 and outside r z: 2.
Do not solve the integral. “If 11' A: a S3 (Hzco‘seﬂzde __ 832.36%
C: l a. 0 7. (15 points) For the curve given parametricaﬂy by x=1+2t2 y=4+t3 (a) Find at 15:1 Eﬁ_: IE§«( Egg 3
dx Ht t“ % dx
'z 21 3..
i1. 3% dis1W .___. ,5“.
dxt it; §qt
dd: (C) The equation of the tangent line throught the
point (3, 3). ' i! 8. (10 points) Find the area under
x:t—sint yzl—cost forOgtS'ZW b b
R1? j Y dx 2‘ E (\mcothS«CD$ED OH: O\ 0. VW j ~2Co§t +CQ§Z“JCT CH;
C) 3+ (2693+ g \~2coae+:i(w) 0U: ...
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This test prep was uploaded on 04/07/2008 for the course MATH 122 taught by Professor Butler during the Spring '07 term at Case Western.
 Spring '07
 Butler
 Math

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