W11_CalcII_test2_Blue_solution

W11_CalcII_test2_Blue_solution - Calculus H Midterm 2 W...

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Unformatted text preview: Calculus H Midterm 2 W 2011 QDL“€ 2 1. (4 mark each; total 12 marks) (a) Suppose that the average waiting time for purchasing tickets at the local movie theater is 4 minutes. Find the probability that a customer will have to wait for tickets more than 6 minutes. 90 b “NH te'tMv l Ark—me I2.» -e"‘"*1 G 6 \o-) co 6 , -b - -:y =QM ~e Aurel/H =e “zoom. baa: C. 0L Qomo = 4— P(o<><<6)= «— Segue 0 -3/L =6 9‘4. OIL 6% Answer: (b) Consider the initial value problem y’ = :L'(1+y)1 with initial value condition y(2) = 1. Use Euler‘s Method with step—size h = 1/2 to approximate was). am“ so xo=l , no” F093): (8/: XC “‘33 8‘ an=6m—I+L‘¥vavu‘3w‘t) )xvx‘7th-“l’im n :13”. 1% o xa=l ‘&‘4 4 “32:. 3‘: warmly): 4+ 314mm» = 3 :4, x1: 3, :81: \3.+L\F(x.,~a\)= 3+ i(%(l+3))= <5 3 X3=% 33: wirinfixwt): grfibtrfim = 9‘5?- Answer: EgLs'Sy’: LL23“ (c) Find rig/rim= r;i2;g/d:1:2 for the polar curve 1" = 2 cos 6. its" 43/419 _ 209929 ><= r009=9~m19 \— afig amaze 5%— c—Lr meme s-a MZG =_u}cle l8=rmixe=2cw9ml~65m3~19 = 2. dial“ = $C§g€l = w 0‘ am e x1 okx —lm~7v~7.9 1. 1, _ 9% r. — Csc 29 Answerl_C$¢$—‘29 M — — Calculus H Midterm 2 W 2011 3 2. (10 marks) Solve the following separable differential equation, isolating for y as an explicit function of :L': 3x2/3y‘r = (23; + 3)COS(:131/3), y(0) = 1/2. 3x743 so ; 3 mx"3 gx 23% 3x”3 k9U--$0!> 03h"! “PX.” A»; -\_=:><.ZI3AX So tQMuvfi - mx‘/’+C\ nova - o1wa ‘\'C2 V; \Lafifl ~ Cselmx 23+?) = (482“ xv; IL ' V3 3: Ce MX ’32- & 3(o)= i} so :=ce°-—:: ,so Calculus II Midterm 2 W 2011 4 3. (8 marks) (a) (3 marks) Find fir: f“; for the function f(:1:, y) = 11:2sec(2y) + yx £x=lxaeclta + Q») = L\x M623 (Eu/~13 -\- X'aX-Ievé + (b) (3 marks) A tank with 80 L of water contains 7kg of salt. Pure water pours into the tank at a rate of 11 L / min, the solution is kept thoroughly mixed and exits the tank at the same rate. SET UP (DO NOT EVAL— UATE) the initial value problem (that is= the differential equation AND the initial value condition) that models this process. LET A=ALQ DEDOTG’ Amount as: SALT A$ A Fume-n6» 94: True ’6 %= AA' OI "’ A4 OR. % :: - Ui'w' A(°)=7~ O (c) (2 marks) Consider the differential equation for which the direction field is shown below. Sketch the solution to the initial value problem with ini- tial condition y(1) = 2 f 2' l / / / Calculus H Midterm 2 W 2011 5 4. (10 marks) Find the area inside one 100p of the polar curve 1" = 2008(29) but outside the curve 7" = 1. Calculus II Midterm 2 W’ 2011 6 5. (10 marks total) Answer the following questions in the Space provided r0 ¢¢ (a) (2 marks) Convert the point with polar coordinates (2, 7r / 6) to Carte- sian coordinates (exact values: not decimal representations). = C 9" ' E = r M 2M ‘ A Answer: (E: l) (b) (2 marks) Convert the polar curve 9*“ = 2cot 9 to a Cartesian equa- tion. one“; So che= 2< xii-‘31:” ing-x—n” =— 14‘— ot. x5an: 9i: 23 a 7. Answer: Xi‘t‘az': LDC/'31 (c) (1 marks) True / False The differential equation 2yy’ — $699 +@: 3 has order 6. Answer; WW5: (d) (2 mark) Find the domain of the function C no refit-talc» . : _ 2 —{-’I?2+y2+32) filiyazl [113 y +6 means x—xaLzo 02. x231 Answer: x— '3‘ 7/ 0 9L xvflal (e) (1 mark) True / False y' = my? — x is a separable difierential equation. ‘8’; Dig; ~_ X ( .314) Answer: 'TQUE (f) (1 mark) True / False 2sin(3x) is a solution of the differential equation y”+9;g = 0. (C ‘3: 1&1» ) I: 372033)» , 0=’3>2‘2'm2a3x=—‘5 la la Elfllnswer:L (g) (1 mark) Let flu: o,w) = 2sin(7m) + wsec(o). Find f(0,7r: 2). QCOflTfl) = *chc-W = ~9— Answer; '1 ...
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This note was uploaded on 10/05/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

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W11_CalcII_test2_Blue_solution - Calculus H Midterm 2 W...

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