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MA 261 - MULTIVARIATE CALCULUS - Purdue Study Resources
  • 2 Pages reduce
    Reduce

    School: Purdue

    function AEQ = reduce(A) %last updated 5/7/94%REDUCE Perform row reduction on matrix A by explicitly choosing% row operations to use. A row operation can be "undone", but% this feature cannot be used in succession.% Use in the form => reduce(A) <=% By: Da

  • 3 Pages Ans-261FE-S2002
    Ans-261FE-S2002

    School: Purdue

    Course: Calculus III

    MA261 Final Exam Spring 2002 1. D 2. A 3. B 4. C 5. E 6. D 7. B 8. A 9. D 10. E 11. C 12. A 13. A 14. C 15. A 16. B 17. A 18. B 19. E 20. D

  • 3 Pages Ans-261FE-F2008
    Ans-261FE-F2008

    School: Purdue

    Course: Calculus III

    MA26100 FinalExamKey 1. E 2. C 3. A 4. D 5. E 6. B 7. E 8. C 9. A 10. E 11. C 12. B 13. C 14. D 15. D 16. B 17. D 18. D 19. E 20. A 21. B 22. A Fall08

  • 1 Page Ans-261FE-F2007
    Ans-261FE-F2007

    School: Purdue

    Course: Calculus III

  • 1 Page Ans-261FE-F2005
    Ans-261FE-F2005

    School: Purdue

    Course: Calculus III

  • 11 Pages 261FE-S2008
    261FE-S2008

    School: Purdue

    Course: Calculus III

    MA 261 FINAL EXAM Form A Spring 2008 1. Find an equation of the plane that contains the point (2, 1, 1) and the line x = 1 + 3t, y = 2 + t, z = 4 + t. A. 3x + y + z = 8 B. 2x + y + z = 6 C. x + 2y + 4z = 8 D. x - 5y + 2z = -1 E. x - 2y + z = 1 2. Compute

  • 9 Pages 261FE-S2003
    261FE-S2003

    School: Purdue

    Course: Calculus III

  • 11 Pages 261FE-S2001
    261FE-S2001

    School: Purdue

    Course: Calculus III

    MATH 261 - SPRING 2001 FINAL EXAM Name Signature Div. Sect. No. Instructor Recitation Instructor FINAL EXAM INSTRUCTIONS 1. You must use a #2 pencil on the mark-sense sheet (answer sheet). 2. On the mark-sense sheet, fill in the instructor's name and the

  • 9 Pages 261FE-S2000
    261FE-S2000

    School: Purdue

    Course: Calculus III

    MATH 261 - SPRING 2000 Name Signature Div. Sect. No. Instructor (Test 01) Recitation Instructor FINAL EXAM INSTRUCTIONS 1. You must use a #2 pencil on the mark-sense sheet (answer sheet). 2. If you have test 01, mark 01 and blacken the corresponding circl

  • 14 Pages 261FE-S1999
    261FE-S1999

    School: Purdue

    Course: Calculus III

    MA 261 NAME STUDENT ID # INSTRUCTOR INSTRUCTIONS FINAL EXAM Spring 1999 Page 1/14 1. There are 14 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. I.D.# is your 9 digit ID (probably

  • 12 Pages 261FE-F2008
    261FE-F2008

    School: Purdue

    Course: Calculus III

  • 14 Pages 261FE-F2007
    261FE-F2007

    School: Purdue

    Course: Calculus III

  • 6 Pages Sol-261E2-S2001
    Sol-261E2-S2001

    School: Purdue

    Course: Calculus III

  • 1 Page Sol-261E2-S2000
    Sol-261E2-S2000

    School: Purdue

    Course: Calculus III

    SPRING 2000 ANSWERS FOR EXAM II: 1. C 2. D 3. B 4. E 5. A 6. (0, 0) saddle, (1, -1) min. /2 1 7. (a) (1/2, 0) (b) r = cos 0 25-x2 0 25-r2 (c) 0 cos r 3 dr d 25-x2 -y 2 8. (a) -1 5 0 z dz dy dx (b) /2 0 3 6-2x 0 0 zrdz dr d. 6-2x-y 9. 0 0 dz dy dx 1

  • 1 Page Sol-261E2-S1999
    Sol-261E2-S1999

    School: Purdue

    Course: Calculus III

    SPRING 1999 ANSWERS FOR EXAM II: 1. E 2. B 3. B 4. B 5. B 6. E 7. D 2 1/2 1-r2 8. 0 0 - 1-r2 r dz dr d 9. 3/2 6 (13 - 1) 10. (1) (3, 3/2) minimum (2) (-2, -1) saddle 1

  • 11 Pages Sol-261E2-F2006
    Sol-261E2-F2006

    School: Purdue

    Course: Calculus III

  • 5 Pages 153E1-F00
    153E1-F00

    School: Purdue

    MA 153 Exam 1 Fall 2000 Name: _ Student ID: _ Instructor: _ Class Hour: _ INSTRUCTIONS: (1) There is no credit for guessing. You must show your work to receive credit! (2) Please fill in all the above information and write your name on the top of each of

  • 5 Pages 153E2-F00
    153E2-F00

    School: Purdue

    MA 153 Exam 2 Fall 2000 Name: _ Student ID: _ Instructor: _ Class Hour: _ INSTRUCTIONS: (1) There is no credit for guessing. You must show your work to receive credit! (2) Please fill in all the above information and write your name on the top of each of

  • 6 Pages 153E3-S02-O
    153E3-S02-O

    School: Purdue

    MA 153 Exam 3 Spring 2002 1. Find the slope, m , and the y -intercept, b , of the line given by the equation 3 x - 4 y = 8 . 3 A. m = - ; b = -2 4 3 B. m = ; b = 8 4 3 C. m = - ; b = 8 4 3 D . m = ; b = -2 4 E . None of the above Use the graph of a functi

  • 4 Pages project
    Project

    School: Purdue

    function project(u,w) %last updated 5/9/94 %PROJECT Projecting vector U onto vector W orthogonally. Vectors % U and W can be either a pair of 2D or 3D vectors. A sketch % showing U being projected onto W is displayed sequentially. % % Use in the form => p

  • 8 Pages practicefinal7
    Practicefinal7

    School: Purdue

    MA 261 PRACTICE PROBLEMS 1. If the line x-1 2 has symmetric equations y -3 = = z+2 7 , find a vector equation for the line A. r = (1 + 2t)i - 3tj + (-2 + 7t)k that contains the point (2, 1, -3) and is parallel to . B. r = (2 + t)i - 3j + (7 - 2t)k D. r =

  • 4 Pages practicefinal
    Practicefinal

    School: Purdue

  • 1 Page pp
    Pp

    School: Purdue

    Phase Portraits - pplane6 The routine pplane6 is already loaded on all PUCC machines as standard software. If you are using your own copy of Matlab you may need to download pplane6. Here is a link : http:/math.rice.edu/dfield/ (Note: pplane5 is an older

  • 1 Page num
    Num

    School: Purdue

    Numerical Methods & .m Files In order to use Matlab routines for the Euler, Improved Euler and Runge-Kutta Methods, you will need the les eul.m, rk2.m and rk4.m, respectively. These les are already present on all PUCC machines as standard software. If you

  • 9 Pages lsqgame
    Lsqgame

    School: Purdue

    %LSQGAME Least Squares Line Game last updated 2/10/96 % % An interactive 'game' to select the least squares line % to a set of data. Two guesses for the lsq line can be made % using the mouse to select two points that are then connected. % The 'true' leas

  • 2 Pages groundbase
    Groundbase

    School: Purdue

  • 1 Page FEx
    FEx

    School: Purdue

  • 1 Page df
    Df

    School: Purdue

    Direction Fields -deld6 The routine deld6 is already loaded on all PUCC machines as standard software. To access it from any PUCC machine: StartAll ProgramsStandard SoftwareComputational PackagesMATLAB6.1MATLAB6.1 If you are using your own copy of Matlab

  • 1 Page ci2
    Ci2

    School: Purdue

  • 2 Pages basic
    Basic

    School: Purdue

  • 1 Page assignment3
    Assignment3

    School: Purdue

  • 1 Page Ans-153E3-F01
    Ans-153E3-F01

    School: Purdue

    MA 153 Exam 3 Answers Fall 2001 1. (a) 6 9 (b) 2 (c) 10 x 3 - 3 2. (a) [- 4,2] (b) [- 3,4] 1 (c) (- 4,-2 ) ( ,2] 3. (4,3)and (- 1,-7 ) 4. g -1 (x ) = 2 x+5 5. 14 7 or or 1.75 8 4 y = f (x - 2 )+ 5 6. -13 7. (2,5) (6,5) (4,2) 8. 2a + h - 1 9. y = - 10 (x -

  • 1 Page Ans-153E1-S03-O
    Ans-153E1-S03-O

    School: Purdue

    Question # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Orange Form D C D A B C A A B D C Answer y-x x x4y6 3z 4 7 4x 9 5 x 3 - 6 x 2 + 5 x - 14 9 x 3 - 24 x 2 + 16 x ( x + 4) x + 2 ( ) 4x3 + 5 b2 + a2 a ( x + 5)( x 2 + 4) x+2 9t - t 2 (t + 4 )( t - 4) x is betwee

  • 1 Page Ans-153E1-F01
    Ans-153E1-F01

    School: Purdue

    MA 153 Exam 1 Answers Fall 2001 1. 6 x 3 + 19 x2 26 x + 5 2. x + 8 x + 15 x 25 3. y = 4. mW gm x 2 x +2 5 (a) 2(3 x + 4)(2 x 1) (b) (4 x + y )(4 x y)(a + 3c) 6. (a) x= -5, 7 (b) x = 6 7. (a) 20 ab11 (b) 3a3b 4 8. 3:00 p.m. 9. 16.4 cm

  • 1 Page Sol-261E2-F1998
    Sol-261E2-F1998

    School: Purdue

    Course: Calculus III

    FALL 1998 ANSWERS FOR EXAM II: 1. B 2. C 3. E 4. A 5. D 6. B 7. E 8. 2 2 9. 0 1 r 4r 2 + 1 dr d= (173/2 - 53/2 ) 6 3/2 3-2x2 5-x2 10. - 3/2 - 3-2x2 dz dy dx 2+x2 +y 2 1

  • 1 Page Ans-261E2-S2009
    Ans-261E2-S2009

    School: Purdue

    Course: Calculus III

  • 1 Page Ans-261E1-S2009
    Ans-261E1-S2009

    School: Purdue

    Course: Calculus III

  • 1 Page Ans-261E1-S2006
    Ans-261E1-S2006

    School: Purdue

    Course: Calculus III

  • 1 Page Ans-261E1-F2008
    Ans-261E1-F2008

    School: Purdue

    Course: Calculus III

  • 1 Page Ans-261E1-F2007
    Ans-261E1-F2007

    School: Purdue

    Course: Calculus III

  • 1 Page Ans-261E1-F2005
    Ans-261E1-F2005

    School: Purdue

    Course: Calculus III

  • 7 Pages 261E1-S2009
    261E1-S2009

    School: Purdue

    Course: Calculus III

  • 6 Pages 261E1-S2002
    261E1-S2002

    School: Purdue

    Course: Calculus III

  • 6 Pages 261E1-S2001
    261E1-S2001

    School: Purdue

    Course: Calculus III

    MA 261 NAME STUDENT ID EXAM 1 Spring 2001 Page 1/6 Page 1 Page 2 Page 3 Page 4 /12 /7 /18 /18 /27 /18 /100 RECITATION INSTRUCTOR RECITATION TIME Page 5 Page 6 TOTAL DIRECTIONS 1. Write your name, student ID number, recitation instructor's name and recitat

  • 9 Pages 261E1-S2000
    261E1-S2000

    School: Purdue

    Course: Calculus III

    MA 261 NAME STUDENT ID # Exam 1 Spring 2000 Page 1/9 RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1) Fill in the above information. Also write your name at the top of each page of the exam. 2) The test has 9 pages, including this one. 3) Problems 1 th

  • 6 Pages 261E1-S1998
    261E1-S1998

    School: Purdue

    Course: Calculus III

    MA 261 NAME STUDENT ID # INSTRUCTOR INSTRUCTIONS EXAM I Spring 1998 Page 1/6 1. There are 6 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your

  • 8 Pages 261E1-F2011
    261E1-F2011

    School: Purdue

    Course: Calculus III

  • 8 Pages 261E1-F2008
    261E1-F2008

    School: Purdue

    Course: Calculus III

  • 5 Pages 261E1-F2000
    261E1-F2000

    School: Purdue

    Course: Calculus III

    MATH 261 FALL 2000 FIRST EXAM September 26, 2000 STUDENT NAME -STUDENT ID -RECITATION HOUR -RECITATION INSTRUCTOR - INSTRUCTIONS: 1. This test booklet has 5 pages including this one. 2. Fill in your name, your student ID number, your recitation hour and y

  • 11 Pages Sol-261FE-S2001
    Sol-261FE-S2001

    School: Purdue

    Course: Calculus III

  • 1 Page Sol-261FE-S2000
    Sol-261FE-S2000

    School: Purdue

    Course: Calculus III

    Answers to MA261 Final (Spring 2000) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. D E C C B A D A D D B C C C C E D E A E

  • 6 Pages Sol-261E1-F1998
    Sol-261E1-F1998

    School: Purdue

    Course: Calculus III

  • 11 Pages Sol-261E1-F2006
    Sol-261E1-F2006

    School: Purdue

    Course: Calculus III

  • 28 Pages Sol-261E1-S1998
    Sol-261E1-S1998

    School: Purdue

    Course: Calculus III

  • 3 Pages Ans-261E2-S2008
    Ans-261E2-S2008

    School: Purdue

    Course: Calculus III

    Exam 2 Answer Key MA 262 Spring 2008 1. C 2. E 3. D 4. B 5. B 6. A 7. D 8. B 9. C 10. E

  • 1 Page Ans-261E2-S2006
    Ans-261E2-S2006

    School: Purdue

    Course: Calculus III

  • 1 Page Ans-261E2-F2011
    Ans-261E2-F2011

    School: Purdue

    Course: Calculus III

  • 1 Page Ans-261E2-F2007
    Ans-261E2-F2007

    School: Purdue

    Course: Calculus III

  • 1 Page Ans-261E2-F2005
    Ans-261E2-F2005

    School: Purdue

    Course: Calculus III

  • 7 Pages 261E2-S2009
    261E2-S2009

    School: Purdue

    Course: Calculus III

  • 7 Pages 261E2-S2003
    261E2-S2003

    School: Purdue

    Course: Calculus III

  • 6 Pages 261E2-S2002
    261E2-S2002

    School: Purdue

    Course: Calculus III

  • 6 Pages 261E2-S2001
    261E2-S2001

    School: Purdue

    Course: Calculus III

    MA 261 NAME STUDENT ID # Exam 2 Spring 2001 Page 1/6 RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1) Fill in the above information. Also write your name at the top of each page of the exam. 2) The exam has 6 pages, including this one. 3) Problems 1 th

  • 8 Pages 261E2-S2000
    261E2-S2000

    School: Purdue

    Course: Calculus III

    MA 261 NAME STUDENT ID # Exam 2 Spring 2000 Page 1/8 RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1) Fill in the above information. Also write your name at the top of each page of the exam. 2) The test has 8 pages, including this one. 3) Problems 1 th

  • 7 Pages 261E2-S1999
    261E2-S1999

    School: Purdue

    Course: Calculus III

    MA 261 NAME STUDENT ID # INSTRUCTOR INSTRUCTIONS EXAM II Spring 1999 Page 1/7 1. There are 7 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your

  • 10 Pages 261E2-F2011
    261E2-F2011

    School: Purdue

    Course: Calculus III

  • 9 Pages 261E2-F2008
    261E2-F2008

    School: Purdue

    Course: Calculus III

  • 6 Pages Sol-261E1-S2001
    Sol-261E1-S2001

    School: Purdue

    Course: Calculus III

  • 10 Pages Sol-261E1-S2000
    Sol-261E1-S2000

    School: Purdue

    Course: Calculus III

  • 11 Pages Ans-261FE-S2008
    Ans-261FE-S2008

    School: Purdue

    Course: Calculus III

    MA 261 FINAL EXAM Form A Spring 2008 Answer Key: 1D 2A 3D 4B 5C 6D 7B 8D 9B 10A 11A 12E 13A 14A 15E 16B 17B 18B 19A 20E 21B 22B 1. Find an equation of the plane that contains the point (2, 1, 1) and the line x = 1 + 3t, y = 2 + t, z = 4 + t. A. 3x + y + z

  • 7 Pages Fall 2013 Exam 1 Solution
    Fall 2013 Exam 1 Solution

    School: Purdue

    Course: MULTIVARIATE CALCULUS

  • 2 Pages Quiz4Solutions
    Quiz4Solutions

    School: Purdue

    Course: Calculus

    Quiz 4 Solutions David Imberti November 28, 2012 (1) (this problem changed slightly for each section) a2 2 xy lim(x,y)(0,0) x +2+y+y x 2 = lim(x,y)(0,0) (x+y) x+y = lim(x,y)(0,0) x + y =0 b2 2xy lim(x,y)(0,0) x x+y+2y x = y, x 0: 2 +2 = limx0 x2x x = 0 x

  • 2 Pages Quiz5
    Quiz5

    School: Purdue

    Course: Calculus

    Quiz 5 David Imberti September 24, 2012 1-Find the tangent plane to x2 + y 2 + z 2 = 1 at (0, 0, 1). 2-The volume of a piece of track is given by V = xyz , where x = 2 in. y = 4 in., and z = 3600 in., you estimate in the heat that the track could expand a

  • 2 Pages Quiz5Solutions
    Quiz5Solutions

    School: Purdue

    Course: Calculus

    Quiz 5 Solutions David Imberti November 28, 2012 (1) This is the top of the sphere. The easiest way to do this is to draw the picture and conclude that z = 1 is the tangent plane. Alternatively: z = + 1 x2 y 2 (positive since the point being considered is

  • 2 Pages Quiz6
    Quiz6

    School: Purdue

    Course: Calculus

    Quiz 6 David Imberti November 28, 2012 (1) Use Lagrangian Multipliers to nd MAXimum of 4x2 + 2y 2 along x2 + y 2 = 1. Calculate (2) (a) 11 exp(2x + 3y )dxdy 00 (b) 11 exp( x )dydx y 0x (Hint: reverse the integration order) 1

  • 2 Pages Quiz6Solutions
    Quiz6Solutions

    School: Purdue

    Course: Calculus

    Quiz 6 Solutions David Imberti November 28, 2012 (1) f = 4x2 + 2y 2 , g = x2 + y 2 1 f =< 8x, 4y >, g =< 2x, 2y > f = g 4x = x 2y = y x2 + y 2 = 1 If x = 0 then since x2 + y 2 = 1, y = 0 and thus = 2 but y 2 = 1, y = 1. Likewise if y = 0 then x = 1. If bo

  • 2 Pages Quiz7
    Quiz7

    School: Purdue

    Course: Calculus

    Quiz 7 David Imberti November 28, 2012 (1) Convert to polar coordinates, and then calculate the integral. 2 1 2y (x + y )dxdy 0y (2) Calculate the surface area of the part of the plane 3x + 2y + z = 6 that lies in the rst octant. 1

  • 2 Pages Quiz7Solutions
    Quiz7Solutions

    School: Purdue

    Course: Calculus

    Quiz 7 Solutions David Imberti November 28, 2012 (1) 1 2y 2 (x + y )dxdy 0y 22 = 04 0 r (cos + sin)drd 2 = ( 04 cos + sin)( 0 r2 ) 3 4 = (sin cos)|0 ( r3 )|sqrt2 0 3 22 =3 (2) z = 6 3x 2y z z x = 3, y = 2 2 2 1 + (3) + (2) dA = 14 dA The area on the xy

  • 2 Pages Quiz8Solutions
    Quiz8Solutions

    School: Purdue

    Course: Calculus

    Quiz 8 Solutions David Imberti November 30, 2012 (1) This problem could be done many ways. One possible way: (a) 2 1 1 2 1 1z rdrdzd 0 0 0 rdrdzd 0 00 (b) You can just use general expressions for the volume of a cone and a cylinder if you dont want to eva

  • 2 Pages Quiz9Solutions
    Quiz9Solutions

    School: Purdue

    Course: Calculus

    Quiz 9 Solutions David Imberti November 28, 2012 We use Greens Theorem directly for both questions. (1) C F dr = A(C ) P + Q dA y x = A(C ) 0dA =0 (2) C F dr = A(C ) P + Q dA y x = A(C ) x2 + y 2 dA Polar Coordinates: 2 100 = 0 0 r3 drd = 2 1 (100)4 4 1

  • 2 Pages Quiz10
    Quiz10

    School: Purdue

    Course: Calculus

    Quiz 10 David Imberti November 27, 2012 (1) Give a parametrization of the shell of a sphere in the rst octant with radius 1. (2) Find F dS with S the surface as in 1 and F = xi + y j + z k (i.e., nd the linear heat ow across S the octalsphere) 1

  • 2 Pages Quiz10Solutions
    Quiz10Solutions

    School: Purdue

    Course: Calculus

    Quiz 10 Solution David Imberti November 28, 2012 (1) This is just the vector equation of the spherical coordinates. r(, ) =< cossin, sinsin, cos > To force this into the rst octant: 0 ,0 . 2 2 (2) This problem is the last example from section 16.7 in the

  • 4 Pages vectoralgebra
    Vectoralgebra

    School: Purdue

    Basic Vector Algebra Denition of a Vector: A vector is an object which is characterized by two properties: length (magnitude) and direction. Vector Algebra: 1. Vector Addition u + v : the result is obtained by means of the triangular- or parallelogram- la

  • 3 Pages SolutionsQ5
    SolutionsQ5

    School: Purdue

  • 3 Pages SolutionsQ4
    SolutionsQ4

    School: Purdue

  • 3 Pages SolutionsQ3
    SolutionsQ3

    School: Purdue

    Quiz 3, Section 171, T 2:30 pm P1. (a) Find the arclenght of the curve: r(t) = (2 sin(t), 5t, 2 cos(t), 0 t 2. (b) If you started at the point (0, 0, 2), and moved 2 29 units along the previous curve, where are you now? Solution: (a) First, lets calculate

  • 2 Pages Quiz4
    Quiz4

    School: Purdue

    Course: Calculus

    Quiz 4 David Imberti November 28, 2012 1-Find if it exists, or show that it does not. 2 2 xy a- lim(x,y)(0,0) x +2+y+y x 2 2xy b- lim(x,y)(0,0) x x+y+2y 2Sketch the level curves of f (x, y ) = c, for f (x, y ) = x2 + y 2 , c = 1, 4. 1

  • 2 Pages Quiz3Solutions
    Quiz3Solutions

    School: Purdue

    Course: Calculus

    Quiz 3 Solutions David Imberti November 28, 2012 (1) One way to do this is to recognize that the rst part of the track is a straight line from (0, 0) to (1, 1) which is thus of length 2, and the other piece is an eighth part of a circle of radius 1 which

  • 2 Pages Quiz3
    Quiz3

    School: Purdue

    Course: Calculus

    DavidImberti September 10, 2012 Quiz 3-show work You are helping design a railroad for good ol Union Pacic, you approximate a model parametric equation for the track as: r(t) = tikm + tjkm for 0 t 1 r(t) = (cos( 34 (t 1) + 1)ikm + (sin( 34 ) (t 1) + 1)jkm

  • 3 Pages MA261quiz_1
    MA261quiz_1

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 1 Spring 2011 Problem 1. Find the angle between the vectors 1, 1, 1 and 1, 1, 2 . (Hint: Look at the dot product of these two vectors.) Since 1, 1, 1 1, 1, 2 = 1 + 1 2 = 0, we know these two vectors are perpendicular. Thus, the angle

  • 3 Pages MA261quiz_2
    MA261quiz_2

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 2 Spring 2011 Problem 1. Given two planes x + y + z = 2 and x + y = 1, (a) Find the two normal vectors associated to each plane, respectively. (Notice that x + y = 1 is the same thing as x + y + 0 z = 1) Solution. We read the normal v

  • 3 Pages MA261quiz_3_solution
    MA261quiz_3_solution

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 3 Spring 2011 Problem. Consider the ellipse x2 y 2 + = 1, z = 0 4 1 in the three dimensional space. One system of parametric equations of it is r(t) = x(t), y (t), z (t) where x(t) = 2 cos t y (t) = sin t , t [0, 2 ]. z (t) = 0 (a) Fi

  • 2 Pages MA261quiz_4
    MA261quiz_4

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 4 Spring 2011 Problem 1. The position function of a particle is given by r(t) = 3 sin t, 3 cos t, 4t . (1) Find the velocity v(t). Solution. v(t) = r(t) = 3 cos t, 3 sin t, 4 . (2) Find the speed |(t)|. v Solution. |v(t)| = 32 + 42 =

  • 2 Pages MA261quiz_5
    MA261quiz_5

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 5 Spring 2011 2 Problem 1 (Spring 2006). If u(x, y ) = yexy , (a) nd ux . 2 2 Solution. ux = yy 2 exy = y 3 exy . (b) nd uxy . 2 2 2 Sollution. uxy = (ux )y = 3y 2 exy + y 3 2xyexy = y 2 exy (3 + 2xy 2 ). Problem 2 (Spring 2001). Give

  • 2 Pages MA261quiz_6
    MA261quiz_6

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 6 Spring 2011 Problem 1. Suppose y is a function of x and they satisfy F (x, y ) = 0. Take the partial derivative with respect to x of both sides of the above equation (Use Chain Rule ) to show that F dy x = F . dx y Proof. Given F (x

  • 3 Pages MA261quiz_7
    MA261quiz_7

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 7 Spring 2011 Problem 1. Given f (x, y ) = x2 y 2 , (a) Find the critical point of f (x, y ). Solution. Setting f (x, y ) to be zero, we have f (x, y ) = fx (x, y ), fy (x, y ) = 2x, 2y = 0, 0 . So, (x, y ) = (0, 0) is the only critic

  • 3 Pages MA261quiz_8
    MA261quiz_8

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 8 Spring 2011 Problem 1 (modied from Problem 2 in the second midterm of Spring 2 2009). We will nd the maximum of f (x, y ) = xy on the ellipse x + y 2 = 1 using the 4 Lagrange multiplier method. 2 (a) Let g (x, y ) = x + y 2 . Write

  • 3 Pages MA261quiz_9
    MA261quiz_9

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 9 Spring 2011 Problem 1 (Test II.8, Spring 2008). [Warning: No use of cell phone browsing the internet during the quiz!] Let D be the part of disk centered at 0 with radius 2 that lies to the right of the line x = 1. Then which of the

  • 2 Pages MA261quiz_10
    MA261quiz_10

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 10 Spring 2011 Problem 1. Find the length of a wire C in the shape of a helix described by the parametric equation C : x = cos t, y = sin t, z = t, 0 t 4 Solution. To get the length of the wire, let us integrate the constant function

  • 3 Pages MA261quiz_11
    MA261quiz_11

    School: Purdue

    Course: Multivariate Calculus

    MA261 0021&0022 Quiz 11 Spring 2011 Problem 1. (a) Given F(x, y ) = y exy , xexy , nd a function f (x, y ) such that f (x, y ) = F(x, y ). Solution. Since we are told f (x, y ) = F(x, y ), we have fx = yexy and fy = xexy . After integrating the rst equali

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