W11_CalcII_test2_White_solution

W11_CalcII_test2_White_solution - Calculus II Midterm 2 W...

Info iconThis preview shows pages 1–5. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Calculus II Midterm 2 W 2011 MHVTG 2 1. (4 mark each; total 12 marks) (a) Suppose that average waiting time for lunch at Burger Thing is 5 minutes. Find the probability that a customer will have to wait less than 4 minutes to get his lunch. q P< Li\= .1. ’t/g — - 47? H "Vs 0 "V? x< S 8 Alt- 6 = —e +6 =i-e, 43053 O 0 Answer; 4— 6“”: (b) Consider the initial value problem y’ = y — 21': with initial value condition y(1) = 0. Use Euler‘s Method with step-size h = 1/3 to approximate Sc} Xa=x)'a.=0 , X“: X“,\‘\’\’\. 3 (an: ‘A-\*L\$(Xw\f3\m) 'C(xl8)= ‘a-Z‘x n 11:1,,L yin. o xo=4 tao=0 4 “a. Wfioacaw o+-‘5(0-9~‘4l= a 2 xz=% Lat; a\+kc(y.,~3.)= -%+§(-%—l‘%)= ’l’f" 3 x was WWW = 43+ as - z. a= _‘\ Answer: 20”)” 3;? (c) Find the length of the curve 3*" = 200st? for 0 g 9 g 7r/5. T x; L=S 6 valance on ‘3 \5LQCpo1'G-VC-lmkeBl «49 7:“— Answer; ’é 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': y’secx = (33; — 1) sin2 3, y(7r) = 4/3. K— was; 3’ = 0965, = ("534) mf‘x cam - "M" .5.— ka C6 +3 . -'$ Now Qwe m laifififi 3g=C€MW+é :9 C:( Calculus II Midterm 2 W 2011 4 3. (8 marks) (a) (3 marks) Find fy, f“; for the function y) = 11:2 sin(2y) + 1'9 = 1 g {‘3 D. x (1323 + x QMx £47: gjx = Rx c413 -\- laxfi"Q.Nx + £3.96 (b) (3 marks) A tank with 100 L of water contains 3kg of salt. Brine with a concentration of salt of 0.05 kg/ L pours into the tank at a rate of 8 L/min, the solution is kept thoroughly mixed and exits the tank at the same rate. SET UP (DO NOT EVALUATE) the initial value problem (that is, the differential equation AND the initial value condition) that models this process. LET A'v'ALQ WEDGE Amwm’ oc SALT A5 A macaw 96: 1M? £- §1$= (Loos ~8-i or. é—fi—=o.q—LA_ [00 ‘25 com \.\J.(.\ A(o\=$ (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) = —1 H\\\\\\\\ //Fff?/// m\\\\\\\\ //Xfff//z H\\\\\\\\ ////i//// H\\\\\\\\ ff/////// ~\\\\\\Q\ ///X///// fl\\\\\\ i x//////xfi flmm\\\\mw _HHHHMRHE gnnénnan; n#///,//f HEHHMHHHA _,—h_,—'Iv_,—'|r-_,—'|r-_,—'l'-_,—'Ir-_,—Iv_,_h_h. Jx////// m \QKNwmu J////////‘ N\ \\\\NH #/// \\\ \\\.\“- //f \\“ 2// \NH 2/f \H //1 \H Calculus H Midterm 2 W 2011 5 4. (10 marks) Find the area inside one 100p of the polar curve 1" = 2 8111(26) but outside the curve 7' = 1. e.» WM GHQI So nwr r=l9~m7w19 =&l S‘T/n I 3%, Mow ALGA = j :LZCQMA'LG) ole ~§ fi-tlcle 1r \\ Al Wu, = a» l M31 “Al Calculus II Midterm 2 W’ 2011 5. (10 marks total) Answer the following questions in the Space provided If" 6 J ¢ (a) (2 marks) Convert the point with polar coordinates (—1,7r/3) to Cartesian coordinates (exact values, not decimal representations). .. ._ _ 1‘: = .. X— f" we - 1 (no 3 i a: (NV-we .1 -'\ = ——3:- Answer: —% VALE) (b) (2 marks) Convert the polar curve 5*“ = sin(26) to a Cartesian equa- tion. rzmue=2meme=—§‘Zf =Zfih 8° 3W=Lx¥ X (we a L x140 yl't‘fiL = 5) CI) = 1 r . OR- Xl‘t 7‘ 3: 2x (8):“. .95) r 9: Answer. C ‘0‘) C 3) (c) (1 marks) True / False The differential equation 2yy’ — $695 +@: 3 has order 5. Answer: CAK$€ FCJUE'EDS z>/O f(:1:,y:z) = lnlm—yl +sinfi 5 News x—VA 76 o (d) (2 mark) Find the domain of the function Answer: X 7‘ “A 2< 27/0 (e) (1 mark) True / False 11323;” = sin(y) is a separable differential equation. 3/ = ()5L ) 05w *3, Answer: TQUE (f) (1 mark) True/ False eos(3;r) is a solution of the differential equation 3;” + Qy = 0. i“ we; owe, 3% —3m'-3» , ‘3”=~"\Coo'sx‘-‘i~a Answer; TILL)? (g) (1 mark) Let f(u,v,w) = 251n(7m) +wsec(v). Find f(3,0, —1). @0393“) = 1M3“ +C~13m0 _= O __‘ Answer; " l =—\ ...
View Full Document

This note was uploaded on 10/05/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

Page1 / 5

W11_CalcII_test2_White_solution - Calculus II Midterm 2 W...

This preview shows document pages 1 - 5. Sign up to view the full document.

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