EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 This examination has 20 multiple choicequestions and two essayquestions Pleasecheck it over and if you find it to be incomplete notify the proctor Do all your supporting calculations in this booklet In caseof a doubtful mark on your answer card we can then check here When you mark your card use a soft lead pencil 2 Erase fully any answers you want to change Problems 1 through 20 are worth one point apiece Each of the two essayquestions is on a separatesheet PUT YOUR NAME ON EACH SHEET Show all your work and indicate clearly your answerto the problem Partial credit will 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 Find 1 t dt fl B cosb t 1 C sin b sin 1 D cosb COB 1 b coo e6 1 In b J lnb 1 1 b b G In eb H c e E sin eb sin 1 F cos eb COB 1 0 0 2 EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 2 Find te1rtdt A t 1 B K I 8J E e l 11 F 11 G l C 21 H I K J c 1f 1I 2 e l 21 I te 1ft fe e c 1t t JT I e 1 T t 11 J ttt e 1 C tr C 7 e 0 EXAM 2 MATH 132 WEDNESDAY OcrOBER 3 Find the approximation by the Trapezoidal Rule with n 3 23 2002 2 to the integral 1 21 dx 1 x 9 16 7 12 29 48 J 1 z Q 8 JX II 48 A 8 C D E F X 2 2 3 11 i 35 I 48 3 J i 1 J f 1 r t t I EXAM 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 2 secondsof a race Find the Simpson sRule estimate of the distance in meters the runner coveredduring those 2 seconds zI 116 J s v t 0 I 0 0 16 EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 5 Determine whether the integral 1 dx J3 x 1 3 is convergentor divergent If it is convergent then find its value A B C D E 3 t k l 2 V H I L J divergent cP 1 dx t I J t I X 1 c fYi t Jt i I t Jif I 3 I r d t f EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 6 6 Evaluate the integral J lnxdx A 2ln 2 B 2ln2 C 2 D 2 E ln2 2 F ln2 2 2 ln 2ln2 1 2ln2 2 J The integral is improperand divergent x dx x 2 EXAM 2 MATH 132 1 dx is convergeot ii 1t ill A i and li B i and ill C i and iv D i and v dxisdiVergeot dx is divergent t IX iv Tdx 2 v U 3 4 r GII II 0 cPt Xi if J J l 1 4 2 D G ii and v f a J ii H ill and iv I lii and v J iv and v I J t i t J v t r a e i 11 t P x dK J X IA I EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 8 8 Find the area of the region enclosedby the curves y X2 and y x I t It 0 1 i 3 xL 3 0 EXAM 2 MATH 132 1 d T WEDNESDAY OCTOBER 23 2002 0 t 0 2 9 EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 10 10 Find the volume of the solid whose base is the circular disk centered at the origin with radius 1 and whose cross sectionsperpendicular to the x axis are squares c rOSJ if I l 0 J t K 3 Q g 5 EXAM 2 MATH 132 WEDNF3DAY OCTOBER 23 2002 u u AnMD PhD lays a human liver along a ruler with one end at 0 and the other end at the 6 inch mark Using an advancedCAT scan technique she is able to determine that a slice made at x inches perpendicular to the ruler has a crosssectional area of A x lx 6 x in2 for eachx along0 x 6 Find the volume in cubicinches of this liver B 12 25 t D C 12 5 D 12 75 E 13 F l3 25 G 13 5 H 13 75 I 14 J 14 25 G J L A l G CI It tp V x 0 3X J J I X X 6 t x f 6 12 EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 11 12 Consider the solid obtained by rotating about the y axis the region bounded by the curves y X3 Y 8 x 0 Find A y the area of the crosssection of the solid made by the plane perpendicular to the y axis at y when 0 y 8 8 l J A 1rY B 1ryl I 1 I 11rY3 1 1rY F 8y G 8yl H 8y 2 I 8yi J 8y2 X u 1 I IJ EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 13 13 Find the length of the curve y x over 1 x 2 1 I f 1 I ol s r 1 q J r 1 l ff J Q1 I s x r 1 J J I I r b et t I So 2 5 14 EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 14 Find the integral which gives the length of the curve x d A 3 jo y3 5tidt t f y ti J x d t 0 t 3 t L 1 D 103v l 5t2dt E loava 3 i2 dt F J Vi 3t2 dt G J v 3 f1 dt H 103 yI dt 1 03 3 2t2dt J t1 L J yIl W dt l to t 1 EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 6 c tD 15 1 3 3 16 EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 c 2 1 1 EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 if 17 An aquarium 6 ft long 1 ft wide and 4 ft high is full of water which weighs 62 5 Ibs ft3 Find the work in ft Ibs neede9 to pump half of the water out of the aquarium 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 6 d L 1 0 ItjIh 13 EXAM 2 MATH 132 WEDNESDAY OCTOBER 23 2002 18 A force of 10 lb is required to hold a spring stretched 5 inches beyond …
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