Midterm 2-2009 (White Version)

Midterm 2-2009 (White Version) - 03%“ E Calculus II...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 03%“ E Calculus II Midterm 2 March, 2009 2 1. (3 marks each; total 9 marks) Answer each question in the space provided. You MUST show your work. a) A tank contains 100 L of brine, with a concentration of 0.3 kg of salt per liter. Pure water enters the tank at a rate of 5 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. What is the amount of salt in the tank, A(Z), as a function of time I? OQA us our A Egg: oag — 3.334; = "—23 2; AC0):0,7>~\00=30\<%. _'b A : C 7_ 8 4° J‘s/L New ACO)=5Q=CL‘€/o 5) C1,:- 30 $9 b) Use Euler’s Method to approximate y(1.2) with step size h : 0.1 for the following initial value problem: y'=x—y, y(1)=0 wPCNgl=§jl= X—‘g- i3(\):0 :2 x0: A, 130:0 x‘: x°+ln= [+O.\= l.\ 3‘: $04, (A Raw.) —. 04040—0): ot\ XL: X\-\-l’\ = \.\+o.\=\\i (6° ‘31?) 30.2)) ‘31: \Aerbx Pm,qu o.\+o.\ (IA-0.0: 0.1 so $0.1): L31=01 l _ _ ' dy _ fi/ c) If x — cost and y — 2s1n(3l), find Ewhen l— f6. Calculus II Midterm 2 March, 2009 3 2. (5 marks) Suppose the average time waiting in line to purchase movie tickets at some CinepleX is 8 minutes. What is the probability of waiting more than 10 minutes? ~¥A HWL fl JA \ _ 1 gm L 4% ¥(+\= 2 e! = e, '8 mth : \— pUzéhB 00 _.§/ : _ \D ~j Mm = Le, «at Z ‘ Agate ‘é o \D _/u> : —— _ 3 -\ W ‘2 I c \- — \m \—C o\'k _|__ -12.; 0 “WW \0 66 _ $3! fie} w =\\m = 6:9" wwo % .{ — <2, ‘0 ’5 304.5 b _ \an ‘ ‘6 “9" W X” a K“: 3 .1 J4 2', {M5 Calculus II Midterm 2 March, 2009 4 3. (9 marks) Suppose that a corpse was discovered in a motel room at midnight and its temperature was 80°F . The temperature of the room is kept constant at 60°F . Two hours later the temperature of the corpse dropped to 75°F . Find the time of death. Note: The temperature of a corpse at time of death is 98.6°F dT Hint: Newton’s Law of Cooling is given by E : k(T _ where T S is the temperature of the surroundings. 3A7 J3:0 AT \Z-.oo AM- olr _ _- j; -kCT \s) k? C\ s; S l &T=X\¢AE).QM\T’T5\= \4§E+C\)lT«T5\=e, ~€ Tb): %o= Ce°+€0 =9 C=ZO So T: 20 86+ éo To FTND \a use T(&)=_7S— C906”) TUJ¢7§= ZQQZki—QO =7 8”: 32%: ‘3: 5’1k1£“%? so l4: fake? gauze 4; mien Tbs):- 2oe"~ Hp : 20~€rflhw£O WE WANT J6“ sou—r THAW l C’Gwi=Q%k Jet W; .2 A = = .5 a as , so LC) Q) +Qo 6121, 2 (L? 20 2 IQN’Z‘LJ: ' 3’ 4431 OLNUHQ$35Q mm LN 3c, ’\‘.O-b 97:240M. Calculus II Midterm 2 March, 2009 5 4. (9 marks) Find the area of one loop of the polar curve 7" Z 2 005(36) . ez. Azg é: HAG.» wAUT COASEQUTNE ANGLES 9\ > I W WHlCL-l (:0. :0 =7 :Lméaeflw => £03739 =0 =71 39:11; :53) .15} 9:32, 3 a 1: 7 e :6 We 7. so Am=l flwfiell 3‘9 ,r /L M = g lap/a1 59 <99 1‘74, TV _ 86_(\+cméeycx9 "WA, 1% T - 11: = l ; (8' Jrf’m’e’fl = T—EJ‘Jb /3 3‘76 Calculus II Midterm 2 March, 2009 6 5. (2 marks each; total 8 marks) Indicate whether each of the following statements is true (T) or false (F) and JUSTIFY your answer. You will receive credit only if your answer is correct AND properly justified. a) All solutions of the differential equation y' : y2 + 5 are increasing fiinctions. Answer: T Q“ g / Justification: % = 31413 7 O b) y : sin x + cosx is a solution of the differential equation y ' — y : 0. Answer: (PALSg Justification: \al/tk :- CCOOX ‘MXB —- (Mx-k—me) = »,Lm}««>c 7‘ O. c) The parametric curve shown below represents the parametric equations x:cost, yzlz. Answer: F ALSg Justification: on (:(LMH , xeL—‘Lrfl , bur xr—cooireL-MQ . (ALSO wlmlmo, ya: x: 4,310 , bUT C\,o) hat on THE crews d) The two parametric curves y : 3 sin I and x : cost can be converted to the 2 Cartesian equation x2 + y— : 1? 9 Answer: T QUE - — 1 - - 1 1 Justification: Mk: A; 7 30 M1}: Jrcm k_ A- Q; + X Calculus II Midterm 2 March, 2009 7 6. (Total 10 marks) Answer each of the following in the space provided. You do NOT have to show your work for this question, but you may do so if you wish (e. g. for part marks in case the final answer is wrong). a) (2 marks) If f(X) = 800x is the force necessary to extend a spring X meters beyond its natural length of 0.1 meters, calculate the work needed to stretch the spring to 0.12 meters. 0,0; 0‘01 OAQ ( W :& %Qox;l>< = LKQQXL] s Lm«L0.01)L—_-_Q-_\C O O b) (2 marks) Set up an integral that calculates the volume of the solid obtained by rotating the curve y : of}, where O S x S 1, about the x-aXis. S‘TTX (ix A(><)=‘IT(\V?<)L d c) (2 marks) Find the length ofthe curve X = 008249, y = sin26, O S 6 S 7! . 1,. ) 1&912W— %%=—Lfifle, figcamfize O l C935: )1’rf‘fiaf31 #134. d) (2 marks) Consider the direction field shown below. fiffff “Hahn ##M/fff eff/ff! fie-r P—fofff r/x zrrf! ff! XXIII! Eff xxrfff Eff ffffff fix fffiff IF? fiilll L. .Illel fffff‘qf'w’f'w—F fifff/zf f f / {Ha-’33 / I“ fffifr‘i—F fffffr—rc-r—F r'lqi—F-J'Fld—Fdd-i—d—F ,/ I I l 'L ‘I. h ‘I. 'I. 'L I f z x .r’" .r" 0° xrxffrr-rq—P _ fxfirru-rw-«r-r- Which of the followin correct answer. differential equations does it correspond to? Circle the ‘ iii) y' iV) y7/y2 / . . / _ ‘7 mar bfipluen on x rm _, 7:0 wee/KX—il i) y'—— y e) (2 marks) Find a Cartesian equation for the curve represented by I” = 2 . _ xp+jlfi% \T::dLU£'CP (22mm 2 creme/JD A-T oils-N ...
View Full Document

Page1 / 6

Midterm 2-2009 (White Version) - 03%“ E Calculus II...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online