222-malekpour-07spex02-v1

222-malekpour-07spex02-v1 - \/U~3loq I MATH 222 APRIL 12,...

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Unformatted text preview: \/U~3loq I MATH 222 APRIL 12, 2007 SHIRIN MALEKPOUR EXAM II TAflMichael Childers D Marc Conrad Name: _____________________________________ -- |:| Patrick Curran DMatija Kazalicki CIJeremy Rouse Section number: _____________________________________ -_ I I I I I I I I 9051.039” Instructions: . Write your name and section number on every answer sheet. . Show your reasoning. You need to show work to get full credit. . Leave your answers in form of \/§ + 7r3, 1n(2), etc. No Calculators are allowed. Circle your final answers. A few formulas . Variation of parameters: yp = u1(:1:)'01(x) + u2(x)112(a:) where + = 0 and + = . A — C’ . . . Rotation of axes: cot 26 = B ;:r = ucos6 — vs1n6; y = us1n6 + 'Ucos6. .sin26 = 1—_C——OS2E and cos20 = iii—SEQ; Conics c = ae, k = g, ellipse b2 + 02 = a2, hyperbola a2 + b2 = c2. u.v = IullvlcosO. [u >< v] = lqulsinH. u-u = |u|2. Integrating factor: ef PCB)“. TAzClMichael Childers El Marc Conrad Name: _________ __’_ _________________________ __ [J Patrick Curran DMatija Kazalicki ‘ DJeremy Rouse I. (10 points.) Using vector method ShOW that the diagonals of a rectangle are of the same length. TAflMichael Childers El Marc Conrad Name: _____________________________________ __ E! Patrick Curran DMatija Kazalicki DJeremy Rouse II. (20 points.) Let A :2 (—1,1,2), B = (2,1,0) and C = (1,0, 2). (A) Write down the parametric equations for the line through points A and B. ‘ (B) Find the equation of the plane containing the three points A, B and C. (C) Find the area of AABC’ TAzElMichael Childers [:1 Marc Conrad Name: _____________________________________ __ [:1 Patrick Curran DMatija Kazalicki DJeremy Rouse III. (20 points.) $2 2 4 + 739- = 1 with the xy-plane. (A) Identify the intersection of g- + (B) Calculate its eccentricity and locate its foci. TAzElMichael Childers [:1 Marc Conrad Name: _____________________________________ __ El Patrick Curran DMatija Kazalicki DJeremy Rouse W IV. (20 points.) Solve the following differential equation: my’+y=lnm, $>0 TA:l:lMichael Childers Cl Marc Conrad Name: _____________________________________ __ El Patrick Curran DMatija Kazalicki DJeremy Rouse V. (20 points.) Solve the following differential equation: (A) y”—4y’+4y=0 (B) yll~_4y/+4y: e21: ‘ TAzflMichael Childers E] Marc Conrad Name: _____________________________________ _- D Patrick Curran EIMatija Kazalicki DJeremy Rouse VI. (20 points.) (A) Graph the curves 7‘ = 2 005(6) and 7" 2 (in the same picture). 1 2 1 (B) Find the area of the region inside r = E but outside of 'r = 2 008(0). TAzClMichael Childers Cl Marc Conrad Name: ______________________ -_; ____________ __ Cl Patrick Curran DMatija Kazalicki DJeremy Rouse VII. (20 points.) (A) Decide if the following series is convergent or not: °° 2"+5 2 3n n=1 (B) If you answered yes to the previous part, find What the series converges to. TAzEIMichael Childers D Marc Conrad Name: _____________________________________ __ CI Patrick Curran DMatija Kazalicki DJeremy Rouse VIII. (20 points.) (A) Find the Maclaurin series for y = 1n(l + as) (B) Decide for What values of ac the series is convergent. 10 ...
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This note was uploaded on 08/08/2008 for the course MATH 222 taught by Professor Wilson during the Fall '08 term at Wisconsin.

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222-malekpour-07spex02-v1 - \/U~3loq I MATH 222 APRIL 12,...

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