EXAM 2, MATH 132WEDNESDAY, OCTOBER 23, 2002This examination has 20 multiple choice questions, and two essay questions. Please checkit over and if you find it to be incomplete, notify the proctor. Do all your supportingcalculations in this booklet. In case of a doubtful mark on your answer card, we can thencheck here. When you mark your card, use a soft lead pencil (#2). Erase fully any answersyou want to change. Problems 1 through 20 are worth one point apiece.Each of the two essay questions is on a separate sheet. PUT YOUR NAME ON EACHSHEET. Show all your work and indicate clearly your answer to the problem. Partial creditwill be given for partially completed solutions. Each of these problems is worth 5 points.There is a total of 30 points for the whole examination.You may use a Mathematics Department approved scientific calculator.You may use a 3 x 5 note card (both sides).(1) Find1.(':'~~t~dt-=)t~1«fl~;;!)(B) cos b(C) sin b - sin 1(D) cosb - COB 1(E) sin ( eb) - sin 1(F) cos{ eb) - COB 1(G) In(eb)(H) coo ( e6)(1) In b(J) lnb - 1b-=>1,.(~c= e;bb~002. EXAM 2, MATH 132 WEDNESDAY, OCTOBER 23,2002(2) Findte1rt dt...,--1t't" JT1['(""e'"'C-.."I-..".e-1("'C(A) £:t!1\"(B) ~'K,I~:8J-.~~::;-:-:-\(~~~~~!~~/(E) ... e--l11"(F) ~11"(G) £=l21\"(H)~(I) ~'K(J) 1I"2-e-+l21\"eT(t""-c--1f---11'J...c-tr-Cttt:I':;7="" e1ftfe--te0()~~EXAM 2, MATH 132WEDNESDAY. OcrOBER 23, 2002'3"(3) Find the approximation by the Trapezoidal Rule with n1 21 -dx1 x2 to the integral:J.. 1-z(A)(8)(C)(D)(E)(F)~(I)(J)/),X: 2;.-r~/JX:('1-J..'f-I?-~-t)t---+1+{9167122948Q8II4823"11:i)35483iEXAM 2, MATH 132 WEDNESDAY, OCTOBER 23,2002.4) A radar gun was used to record the speed v (in fils) of a runner during the first 2seconds of a race:Find the Simpson's Rule estimate of the distance in meters the runner covered duringthose 2 seconds.116I-.zJs-v--16-I;)0-t (0+-£0~...---EXAM 2, MATH 132WEDNESDAY, OCTOBER 23,2002$(5) Determine whether the integral:1-dxJ3 (x - 1)3is convergent or divergent. If it is convergent, then find its value.-3..,--~-----...---L--(A) ~(B) ~(C) t(D) k(E) *~l-~@2,V(H) ~(I) ~(J) divergent-t-cPI,~-t"-I&dx--()~ J1--(X' -"-1-cfYi.t-Jt:i>..-~...3--I,~I-:r'\.-~---d ('t -f).t;;-JifI--6 EXAM 2, MATH 132 WEDNESDAY, OCTOBER 23, 2002(6) Evaluate the integral J:lnxdx.(A}2ln 2(B) -2ln2(C) 2(D) -2(E) ln2+ 2(F) ln2 - 2~,ln ~ !~2-([~2ln2-~(1) -2ln2 + 2(J) The integral is improper and divergent.x-dx-x--2.EXAM 2, MATH 132ii)ill)iv)1~ ~ dx is convergeot (i)t ~dxisdiVergeot @1~ -!, dx is divergent ~IX t:;>,[;Tdx=2 U/[~.~ 0cPtXi'34v)(A) i) and li).(B) i) and ill).(C) i) and iv).(D) i) and v).J~J.!l~~1~4~2!D(G) ii) and v).(H) ill) and iv).(I) lii) and v).(J) iv) and v).r~GII II- "-/f-'~a"Jif/)ii)I"'; )t..<»J v .t r a e.i11)[~J't')t::P:;J.--X IA..dK~---x~----I8EXAM 2, MATH 132 WEDNESDAY, OCTOBER 23,2002(8) Find the area of the region enclosed by the curves y = X2 and y = x.~/'I~xL.-)...)(---3(--t0It:::0---i1-3-~EXAM 2, MATH 132WEDNESDAY, OCTOBER 23, 20029- /2-- )(::t/0)d~T-+(--1.---:;;>0--10EXAM 2, MATH 132 WEDNESDAY, OCTOBER 23, 2002(10) Find the volume of the solid whose base is the circular disk centered at the originwith radius 1, and whose cross-sections perpendicular to the x-axis are squares.ifc rOSJIl~==-0--£:::)-(J3 ~-gQ-5t{K-;).~EXAM 2, MATH 132WEDNF3DAY. OCTOBER 23, 2002u(u) AnMD-PhD lays a human liver along a ruler with one end at 0 and the other end atthe 6 inch mark. Using an advanced CAT scan technique, she is able to determinethat a slice made at x inches, perpendicular to the ruler, has a cross sectional area ofA(x) = lx(6 - x) in2, for each x along 0 $: x $: 6. Find the volume (in cubic inches)of this liver.(&:~~) J-L - ~(B ) 12 . 25 t ~ ;- G(C) 12.5 D(D) 12.75 I / X)(E) 13 G-,CI(It A(~l'=,- X ( 6-(F).l3.25(G) 13.5 tp(H) 13.75V -(I) 14 )"(J) 14.25t.--x~0x'f""[ 3X{J~612-.::?~)-"J.- ~..11EXAM 2, MATH 132 WEDNESDAY, OCTOBER 23, 2002(12) Consider the solid obtained by rotating about the y-axis the region bounded by thecurvesy = X3, Y = 8, x = 0Find A(y), the area of the cross section of the solid made by the plane perpendicularto the y-axis at y, when 0 ~ y ~ 8. '8~:l J..;;--(A) 1rY(B) 1rylI"")-I1'/1~1-1rY3, .. 1rY"(F) 8y(G) 8yl(H) 8y!2(I) 8yi(J) 8y2X;u1-I/IJ"'"--~--EXAM 2, MATH 132WEDNESDAY, OCTOBER 23, 200213(13) Find the length of the curve y = ~x + ~ over1$x$21..I~-.1~ .::...f--.ol..s--q'\..I'-r-~1+~:r-.J--1...'l.-s-rx.ffJ---I--(I~-r-+~J1°J------~)b..et~-t"~Q1:-~So2-)(("I'/~ )(-I)~5--~-EXAM 2, MATH 132 WEDNESDAY, OCTOBER 23, 200214(14) Find the integral which gives the length of the curvex = t - f, y = ~ti, 0 ~ t .$ 31/",(A) ,"3d~~~'"tJ,x-d't----t.;L1,...t1.f1,--(~)- jo y3 + 5tidt(D) 103 v'l + 5t2 dt(E} loa va-+3'i2 dt(F) J: Vi+3t2 dt(G) J:v'3~ dt3(H) 10 .yI~ dt(1) [03";3 + 2t2 dt(J) J: .yIl+W dtL?l....toEXAM 2, MATH 132WEDNESDAY, OCTOBER 23,2002151.3.3c:')tD-6----EXAM 2, MATH 132 WEDNESDAY, OCTOBER 23,200216<1--1~ (2.)c==EXAM 2, MATH 132WEDNESDAY, OCTOBER 23, 2002if(17) An aquarium 6 ft long, 1 ft wide and 4 ft high is full of water (which weighs 62.5Ibs/ft3). Find the work (in ft-Ibs) neede9 to pump half of the water out of theaquarium over the top edge. /-- ~ =0(A) 749 ///'"~~ ~5 ~'"<r22_~D /; "(D) 750.5 ,..-(E) 751(F) 751.5(G) 752(8) 752.5(1) 153(J) 753.5{If(--"()~')..f((;--d8-'d6'L,.1.0--... - -Itj Ih--13EXAM 2, MATH 132 WEDNESDAY, OCTOBER 23, 2002(18) A force of 10 lb is required to hold a spring stretched 5 inches beyond its naturallength. Find the amount of work done (in inch-pounds) to stretch it from its naturallength to 6 inches beyond its natural length.(A) 32(B) 33(C) 34~D35 ) 36(F 37(G) 38(H) 39(I) 40{J} 41- -J- -,"':-':X:::6V'~{"X:l.i--/0~6-.,~J'O(,--~xd-e.,wf()16--l'WEDNESDAY, OCTOBER 23,2002EXAM 2, MATH 132(19) Suppose the waiting time for a customer's call to be answered by a company followsan exponentially decreasing density. If the average waiting time is 3 minutes, findthe probability that a customer waits more than 6 minutes.(;/~e:J<fv_-t:/,~fdr-e6)~-(A) e-i(B) ~e-i(C) e-l(D) ~e-f(E)e-t(F) ~e-!(G) e-J1W.J~~(J!l!::-;(J) ~e-2{,~-c-"1"e--e--~6-~EXAM 2, MATH 132 WEDNESDAY, OCTOBER 23, 200220(20) Iff(t)c if 0 .$: t .$: 25,l 0 otherwise.is a probability density function, find the value of the constant c.(A) 1(B) ~(C) 13(D) !(E) ~(F) ft~G .l..H) i\30(J) isc;t; .'(
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