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### 243sugprob03long

Course: MATH 243, Spring 2012
School: Delaware
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243, Math Sections 013 and 015, Spring 2012 Suggested discussion problems, Feb 28th or Mar 1st 1. Find an equation of the plane that passes through the point (6, 0, 2) and contains the line x = 4 2t, y = 3 + 5t, z = 7 + 4t. 1 2. Sketch the region bounded by the surfaces z = for 1 z 2. 2 x2 y + 2 and x2 + y 2 = 1 3. Sketch the region bounded by the paraboloids z = x2 + y 2 and z = 2 x2 y 2 . 3 4. Sketch...

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243, Math Sections 013 and 015, Spring 2012 Suggested discussion problems, Feb 28th or Mar 1st 1. Find an equation of the plane that passes through the point (6, 0, 2) and contains the line x = 4 2t, y = 3 + 5t, z = 7 + 4t. 1 2. Sketch the region bounded by the surfaces z = for 1 z 2. 2 x2 y + 2 and x2 + y 2 = 1 3. Sketch the region bounded by the paraboloids z = x2 + y 2 and z = 2 x2 y 2 . 3 4. Sketch the graph of the space curve r(t) = t, t2 , et . Also nd its curvature (as a function of t). (Note that the computations may be messy, and Maple may be of some help.) 4
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Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Feb 28th or Mar 1st1. Find an equation of the plane that passes through the point (6, 0, 2)and contains the line x = 4 2t, y = 3 + 5t, z = 7 + 4t.2. Sketch the region bounded by
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Mar 6th or Mar 8th1. Find the length of the curve r(t) = 12t, 8t3/2 , 3t2 from t = 0 to t = 1.(Hint: Note that 144 + 144t + 36t2 = 36(4 + 4t + t2 ) is a perfect square.)12. Fin
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Mar 6th or Mar 8th1. Find the length of the curve r(t) = 12t, 8t3/2 , 3t2 from t = 0 to t = 1.(Hint: Note that 144 + 144t + 36t2 = 36(4 + 4t + t2 ) is a perfect square.)2. Find
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Mar 13th or Mar 15th1. Find the limit, or show that it does not exist.xy cos y(x,y )(0,0) x2 + y 2lim12. Find the limit, or show that it does not exist.x2 y 2(x,y )(0,0) x2
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Mar 13th or Mar 15th1. Find the limit, or show that it does not exist.xy cos y(x,y )(0,0) x2 + y 2lim2. Find the limit, or show that it does not exist.x2 y 2(x,y )(0,0) x2 +
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Mar 20th or Mar 22nd1. Givenz = x2 + xy 3x = uv 2 + w3y = u + vewnd each of the derivativesz zz,, andwhen u = 2, v = 1, and w = 0.u vw12. Consider the surface dened b
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Mar 20th or Mar 22nd1. Givenz = x2 + xy 3x = uv 2 + w3y = u + vewnd each of the derivativesz zz,, andwhen u = 2, v = 1, and w = 0.u vw2. Consider the surface dened by
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Apr 3rd or Apr 5th1. Find all local maxima, local minima, and saddle points of the functionf (x, y ) = x3 y + 12x2 8y .12. Find all local maxima, local minima, and saddle point
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Apr 10th or Apr 12th13ex+3y dx dy .1. Evaluate0012. Evaluate the integralcos(x + 2y ) dARwhere R is the region dened by 0 x and 0 y /2.23. Evaluate the integralx3 dA
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Apr 10th or Apr 12th13ex+3y dx dy .1. Evaluate002. Evaluate the integralcos(x + 2y ) dARwhere R is the region dened by 0 x and 0 y /2.3. Evaluate the integralx3 dADwh
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Apr 17th or Apr 19th1. Evaluate the iterated integral.311z 2zey dx dz dy00012. Evaluate the triple integralxy dVEwhere E is the solid bounded by the parabolic cylinder
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Apr 17th or Apr 19th1. Evaluate the iterated integral.311z 2zey dx dz dy0002. Evaluate the triple integralxy dVEwhere E is the solid bounded by the parabolic cylinders
Delaware - MATH - 243
Math 243, U of D, Spring 2012Instructor: Idris Mercer, Ewing 529, idmercer@math.udel.eduOce hours: Tuesdays and Thursdays, 2:304:30, or by appointment.Course webpage: http:/www.math.udel.edu/idmercer/243.htmlPrerequisite: Math 242 or equivalent.How y
Delaware - MATH - 243
Math 243 Homework 1 Answers(due Wednesday February 15th)1. Equation of sphere is(x 1)2 + (y + 4)2 + (z 3)2 = 25.To nd intersection of sphere with xz -plane, let y = 0.(x 1)2 + (0 + 4)2 + (z 3)2 = 25(x 1)2 + 16 + (z 3)2 = 25FINAL ANSWER: Circle in x
Delaware - MATH - 243
Math 243 Homework 1Due Wednesday February 15th, in lecture1. Find an equation of the sphere with center (1, 4, 3) and radius 5. Whatis the intersection of this sphere with the xz -plane?2. Find an equation of the sphere that passes through the point (
Delaware - MATH - 243
Math 243 Homework 1Due Wednesday February 15th, in lecture1. Find an equation of the sphere with center (1, 4, 3) and radius 5. Whatis the intersection of this sphere with the xz -plane?2. Find an equation of the sphere that passes through the point (
Delaware - MATH - 243
Math 243 Homework 2 Answers(due Wednesday February 22nd)1a. Let v =Then3, 1 , let w = 0, 5 , and let be the angle between them.vw0+551===|v| |w|2523 + 1 0 + 25so FINAL ANSWER is = = 60 .3cos =1b. Let v = 4, 0, 2 , let w = 2, 1, 0 , and
Delaware - MATH - 243
Math 243 Homework 2Due Wednesday February 22nd, in lecture1a. Find the angle between the vectors3, 1 and 0, 5 in R2 .1b. Find the angle between the vectors 4, 0, 2 and 2, 1, 0 in R3 .12. Find the three angles of the triangle whose vertices are A = (
Delaware - MATH - 243
Math 243 Homework 2Due Wednesday February 22nd, in lecture1a. Find the angle between the vectors3, 1 and 0, 5 in R2 .1b. Find the angle between the vectors 4, 0, 2 and 2, 1, 0 in R3 .2. Find the three angles of the triangle whose vertices are A = (0,
Delaware - MATH - 243
Math 243 Homework 3 Answers(due Wednesday February 29th)1a. Let be the desired line. Since must be perpendicular to the planex y + 3z = 7, a direction vector for is the normal vector to that plane,which is 1, 1, 3 . Therefore can be described asx, y,
Delaware - MATH - 243
Math 243 Homework 3Due Wednesday February 29th, in lecture1a. Find parametric equations for the line through (2, 4, 6) that is perpendicular to the plane x y + 3z = 7.1b. In what points does that line intersect the coordinate planes?12. Let 1 be the
Delaware - MATH - 243
Math 243 Homework 3Due Wednesday February 29th, in lecture1a. Find parametric equations for the line through (2, 4, 6) that is perpendicular to the plane x y + 3z = 7.1b. In what points does that line intersect the coordinate planes?2. Let 1 be the li
Delaware - MATH - 243
Math 243 Homework 4 Answers(due Wednesday March 7th)1(i). For every point on the given curve, we have x = t, y = 0, and z = 2tt2 .If such a point is also on the given paraboloid, it also satises z = x2 + y 2 ,so we have2t t2 = t2 + 022t t2 = t22t 2
Delaware - MATH - 243
Math 243 Homework 4Due Wednesday March 7th, in lecture1(i). At what points does the curve r(t) = t, 0, 2t t2 intersect theparaboloid z = x2 + y 2 ?1(ii). At what points does the helix r(t) = cos t, sin t, t intersect the spherex2 + y 2 + z 2 = 10?1
Delaware - MATH - 243
Math 243 Homework 4Due Wednesday March 7th, in lecture1(i). At what points does the curve r(t) = t, 0, 2t t2 intersect theparaboloid z = x2 + y 2 ?1(ii). At what points does the helix r(t) = cos t, sin t, t intersect the spherex2 + y 2 + z 2 = 10?2.
Delaware - MATH - 243
Math 243 Homework 5 Answers(due Wednesday March 14th)1. I is C, II is A, III is B2. The limit does not exist. For example:If (x, y ) (0, 0) along the path y = 0, theny40=00=4x4 + 3 y 4x +0but if (x, y ) (0, 0) along the path y = x, thenx4x41
Delaware - MATH - 243
Math 243 Homework 5Due Wednesday March 14th, in lecture1. Match the pictures I, II, III to the equations A, B, C.IA: z = (x2 y 2 )2IIIIIB: z = sin(x + y )1C: z =11 + x2 + y 2In questions 24, nd the limit or show that it does not exist.2.y4(
Delaware - MATH - 243
Math 243 Homework 5Due Wednesday March 14th, in lecture1. Match the pictures I, II, III to the equations A, B, C.IIIA: z = (x2 y 2 )2B: z = sin(x + y )IIIC: z =11 + x2 + y 2In questions 24, nd the limit or show that it does not exist.2.y4(x,
Delaware - MATH - 243
Math 243 Homework 6 Answers(due Wednesday March 21st)z1(i). To nd zx =, we start with the equation yz = ln(x + z ) and takexof both sides. Remember that this means we treat x as the independentxvariable, y as a constant, and z as a function of x.
Delaware - MATH - 243
Math 243 Homework 6Due Wednesday March 21st, in lecture1 and 2. Consider the surface dened by the equationyz = ln(x + z ).(1)Note that (x, y, z ) = (1, 2, 0) is a point on this surface. The equation (1)implicitly denes z as a function of x and y nea
Delaware - MATH - 243
Math 243 Homework 6Due Wednesday March 21st, in lecture1 and 2. Consider the surface dened by the equationyz = ln(x + z ).(1)Note that (x, y, z ) = (1, 2, 0) is a point on this surface. The equation (1)implicitly denes z as a function of x and y nea
Delaware - MATH - 243
Math 243 Homework 7 Answers(due Wednesday April 11th)1. First note that we havefx = 1 + 2xy + y 2fy = 1 + x2 + 2xyFor a critical point, both of the following equations must be true:1 + 2xy + y 2 = 01 + x2 + 2xy = 0(i)(ii)There may be more than o
Delaware - MATH - 243
Math 243 Homework 7Due Wednesday April 11th, in lecture1. Find all critical points of the functionf (x, y ) = x + y + x2 y + xy 2and classify them as local maxima, local minima, or neither.12. Find all critical points of the functionf (x, y ) = 2x3
Delaware - MATH - 243
Math 243 Homework 7Due Wednesday April 11th, in lecture1. Find all critical points of the functionf (x, y ) = x + y + x2 y + xy 2and classify them as local maxima, local minima, or neither.2. Find all critical points of the functionf (x, y ) = 2x3 +
Delaware - MATH - 243
Math 243 Homework 8Due Wednesday April 18th, in lecture1 and 2. Consider the surface dened by the equationsin(xyz ) = x + 2y + 3z.Note that the above equation implicitly denes z as a function of x and y .1. Find general expressions for the partial de
Delaware - MATH - 243
Math 243 Homework 8Due Wednesday April 18th, in lecture1 and 2. Consider the surface dened by the equationsin(xyz ) = x + 2y + 3z.Note that the above equation implicitly denes z as a function of x and y .1. Find general expressions for the partial de
Delaware - MATH - 243
M at.li 243 Section 013: Test #1NAME:This test has 6 questions on 6 pages.The p oints per page arc ( &gt;. G, 7, 7, 7, 7.Show your work. A c orrect answer w ith little o r no r easoning m ay receive3 p oints Q uestion l a.F ind t he a ngle b etween t h
Delaware - MATH - 243
M ath 243 S ection 015: Test, #1NAME: __This test lias 6 questions on 6 paj;es.The p oints p er p aj^e arc 0, 6, 7, 7, 7, 7.Show your w ork. A c orrect a nswer w ith l ittle o r no r easoning n iny r eceivea l ow score. ( However, there i s no noed
Delaware - ELEG - 305
ELEG305 COMPUTER ASSIGNMENT #1Due Thursday April 5, 2012DIGITAL SIGNAL PROCESSING TECHNIQUESFOR IMPLEMENTATION OF ACOUSTIC EFFECTSCONTENTS(This assignment is courtesy of Prof. Meritxell Lamarca.)A) INTRODUCTIONOne of the most successful application
Delaware - ELEG - 305
ELEG305-HW2ELEG305 Homework Solution #21.15 (Regular Section)(a) The output signal from S1 is sent to S2 as an input. Therefore,1y2 [n] = x2 [n 2] + x2 [n 3]21= y1 [n 2] + y1 [n 3]21= 2x1 [n 2] + 4x1 [n 3] + (2x1 [n 3] + 4x1 [n 4])2= 2x1 [n 2
Delaware - ELEG - 305
ELEG305-HW4ELEG305 Homework Solution #43.4 (Regular Section)T=2, therefore according to (3.39),ak =1T1=21=2x(t)ejk0 t dtT2x(t)ejkt dt01023 jkt1edt +223( )ejkt dt213=(1 ejk )2kj3[1 (1)k ]=2kj3.8Since x(t) is real and
Delaware - ELEG - 305
ELEG305 Signals and SystemsELEG305 Homework Solution #53.29 (Regular Section)(a) N = 8.kk3k3kk3ke j 4 + e j 4e j 4 e j 4ak = cos( ) + sin()=+4422j1 jk N04. Therefore the signal with FSWe know that, for N = 8, the FS coecients for [n
Delaware - ELEG - 305
ELEG305 Signals and SystemsELEG305 Homework Solution #64.6 (Regular Section)FT(a) We know from table 4.6 that x(t) X (j ).FTFTTherefore x(1 t) = x(t 1) ej X (j ), x(1 t) = x(t + 1) ej X (j ). SoFTx1 (t) ej X (j ) + ej X (j ) = 2X (j ) cos( )FT(
Delaware - ELEG - 305
EXAM #2ELEG 305 SIGNALS AND SYSTEMSSPRING 2012Name: _Major: _Read each problem carefully before you start.The problems are NOT equally weighted.Closed book.No calculators, no cellphones.Problem #1 (20 points)The Fourier coefficients, ak, for a p
Delaware - ELEG - 305
Delaware - ELEG - 305
ELEG 305 SIGNALS AND SYSTEMSASSIGNMENT #1 due Tuesday February 14Read Chapters 1 and 2 in Oppenheim, Willsky, and NawabDo Problems #1.3 (a,d,f), #1.9 (b,c), #1.21 (d,e), #1.22 (d,e), #1.25 (c,d), #1.26 (c,d), #1.55 (a,d,e)*ASSIGNMENT #2 due Tuesday F
Delaware - ELEG - 305
ELEG 305 SIGNALS AND SYSTEMSHONORSASSIGNMENT #1 due Tuesday February 14Read Chapters 1 and 2 in Oppenheim, Willsky, and NawabDo Problems #1.3 (a,d,f), #1.9 (b,c), #1.21 (d,e), #1.22 (d,e), #1.25 (c,d), #1.26 (c,d),#1.37 (Correlation Function - Defini
Delaware - ELEG - 305
ELEG 305 SIGNALS AND SYSTEMSASSIGNMENT #4 due Thursday March 15Read Chapter 3 in Oppenheim, Willsky, and NawabDo Problems #3.4, #3.8, #3.22, #3.23, #3.24, #3.26*ASSIGNMENT #5 due Thursday March 22Read Chapter 4 in Oppenheim, Willsky, and NawabDo Pr
Delaware - ELEG - 305
ELEG 305 SIGNALS AND SYSTEMSHONORSASSIGNMENT #4 due Thursday March 15Read Chapter 3 in Oppenheim, Willsky, and NawabDo Problems #3.8, #3.22, #3.23, #3.24, #3.26,#3.65 (Orthogonal representations)*ASSIGNMENT #5 due Thursday March 22Read Chapter 4 i
Delaware - ELEG - 305
ELEG 305 SIGNALS AND SYSTEMSASSIGNMENT #8 due Thursday April 19Read Chapter 9 in Oppenheim, Willsky, and NawabDo Problems #9.5, #9.6, #9.7, #9.21 (a,c,d,g,i), #9.22 (a,c,e,g)*ASSIGNMENT #9 due Thursday April 26Read Chapter 10 in Oppenheim, Willsky,
Delaware - ELEG - 305
ELEG 305 SIGNALS AND SYSTEMSHONORSASSIGNMENT #8 due Thursday April 19Read Chapter 9 in Oppenheim, Willsky, and NawabDo Problems #9.6, #9.7, #9.21 (a,c,d,g,i), #9.22 (a,c,e,g)State-Space Analysis: Read Lathi Sections 10.1-10.2, Do Problem #10.2-2*AS
Delaware - ELEG - 305
UNIVERSITY OF DELAWAREELEG 305SIGNALS AND SYSTEMSSPRING 2012TUESDAY-THURSDAY 12:30 PM - 1:45 PM KIRKBRIDE 004MONDAY 9:05 AM 9:55 AM WILLARD 007INSTRUCTOR:Dr. Leonard J. Cimini, Jr.217A EvansTel: 302-831-4943Email: cimini@ece.udel.eduOffice Hour
Delaware - ELEG - 305
Delaware - ELEG - 305
Delaware - ELEG - 305
Delaware - ELEG - 305
SAMPLE EXAM #3ELEG 305SPRING 2012Problem #1 (25 points)Consider a continuous-time LTI system with transfer functionH ( s) a.)b.)c.)d.)e.)3s s22Determine the poles and zeros.Determine the three possibilities for the region of convergence.Fi
Delaware - ELEG - 305
Delaware - ELEG - 305
Delaware - ELEG - 305
Delaware - CHEM - 322
Chem 332Spring 2012Homework #1Due 10 a.m.Monday, Feb 13thName_1. (10 points) Deduce the structures of A and B, and name A and B.H+ / - H2ONaBH4OBAC6H12OOH13CC6H1013CNMR: 69.5, dcyclohexanolNMR: 127.3, d (2)cyclohexene2. (10 points) Usi
Delaware - CHEM - 322
Chem 332Spring 2012Homework #2Due 10 AM Monday Feb 20thName_Key_1. (10 points) Using any piece that contributes three or fewer carbons to the nal product,outline a method for the conversion of A to B.OCO2CH3OCO2CH3BrH+/H2OONaH2. (10 points)