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Cornell - AEM - 1200
AEM1200, Introduction to Business Management.Friday 2/10AccountingAccounting and the accounting profession Financial statements: the balance sheet Financial statements: the income statementAccountingThe recording, classifying, summarizing, and interp
Cornell - ILR - ILR2020
1) The companys contractual responsibility is to fill this job position with the best qualifiedemployee from the callback list, if the job is not filled by procedure described in Article 10.1.(a),(b) or (c). The company may hire a new employee if in the
Delaware - MATH - 341
M ath 311 S ection O i l : F inal K xainNAMK:This t ost h as 1 2 q uestions o n 1 2 pages, p lus a b lank p a^e a t t he e ndThe p oints p er p a^e a n 1 5, 5. 5,5, B. ( >,(). ( i,(>, G .(i,(i..r> p oiulsj 1 . F ind I he g eneral s olution ol t i n 1
Delaware - MATH - 341
fad'- [5oiAc^3/~ 2H3-/' ^ pr- 23 -V233Math 341 Section O il: Test #3This test has 6 questions on 6 pages. Each page is worth the same.1. Let B be the ordered basis cfw_ ui,u 2 where U T =[3 points] la. Find the coordinates of31/fc . /
Delaware - MATH - 341
Math 341 Section 011: Test #1This test has 6 questions on 6 pages. Each question is worth the same.1. Find the general solution of the dierential equationdy+ 6xy 2 = 0.dx12. Solve the initial value problemxy + 3y = 5x2 ,2y (2) = 5.3. Solve the
Delaware - MATH - 341
Math 341 Section 011: Test #2This test has 6 questions on 6 pages. Each question is worth the same.1. Solve the system10011011101000110101 0x10 x2 01 1 x3 = 0 1 x4 00x5012. Compute the product143 320 1 4 1 1002 452
Delaware - MATH - 341
Math 341 Section 011: Test #3This test has 6 questions on 6 pages. Each page is worth the same.1. Let B be the ordered basis cfw_u1 , u2 where u1 =34and u2 =.23[3 points] 1a. Find the coordinates of5with respect to B .4[3 points] 1b. Find th
Delaware - MATH - 341
Math 341 Section 011: Final ExamNAME:This test has 12 questions on 12 pages, plus a blank page at the end.The points per page are 5,5,5,5,6,6,6,6,6,6,6,6.[5 points] 1. Find the general solution of the dierential equationdy= y cos x.dx1[5 points]
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday February 7th1a. Expand (x 2)3 .1b. Expand and simplify:x2 + x + x2 + x x) (xx2 + x + x1c. By trying large values of x such as x = 1000, guess the limit of the above
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday February 7th1a. Expand (x 2)3 .1b. Expand and simplify:x2 + x + x2 + x x) (xx2 + x + x1c. By trying large values of x such as x = 1000, guess the limit of the above
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday February 14th1. Evaluate the limit.x sin xx0 x tan xlim12. Evaluate the limit.lim x+x02x3. Find the area bounded by the curves y = |x| and y = x2 2.34. Let A
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday February 14th1. Evaluate the limit.x sin xx0 x tan xlim2. Evaluate the limit.lim x+xx03. Find the area bounded by the curves y = |x| and y = x2 2.4. Let A be the
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday February 21st1. Let A be the region bounded by y = x and y =obtained by revolving A around the line y = 1.1x. Find the volume2. Let A be the region bounded by x = 1 +
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday February 21st1. Let A be the region bounded by y = x and y =obtained by revolving A around the line y = 1.x. Find the volume2. Let A be the region bounded by x = 1 + y
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday February 28th1a. Evaluateln x dx.1b. Evaluatearcsin x dx.1 /22a. Evaluatecos2 x dx.0 /22b. Evaluatecos4 x dx.0 /22c. Evaluatecos5 x dx.023. Evaluatex co
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday February 28th1a. Evaluateln x dx.1b. Evaluatearcsin x dx. /22a. Evaluatecos2 x dx.0 /22b. Evaluatecos4 x dx.0 /22c. Evaluatecos5 x dx.0x cos2 x dx.3. Eval
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday March 6th1. Evaluate1dx.x ln x12. Evaluate(sin x + cos x)2 dx.213. Evaluate1earctan xdx.1 + x234. Evaluate02/2x2dx.1 x24
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday March 6th1. Evaluate1dx.x ln x2. Evaluate(sin x + cos x)2 dx.13. Evaluate14. Evaluate0earctan xdx.1 + x22/2x2dx.1 x2
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday March 13th51. Evaluate51dx.x12. Use the Trapezoid rule and Simpsons rule to approximate the integralusing n = 4 subintervals.1 cos(x)dxx+1023. Use Newtons me
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday March 13th51. Evaluate51dx.x2. Use the Trapezoid rule and Simpsons rule to approximate the integralusing n = 4 subintervals.1 cos(x)dxx+103. Use Newtons method
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday March 20th1111. Find the length of the curve y = x3 + x1 between x = and x = 1.62212a. Does the sequence cfw_cos(n ) approach a limit?n=12b. Does the sequence cf
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday March 20th1111. Find the length of the curve y = x3 + x1 between x = and x = 1.6222a. Does the sequence cfw_cos(n ) approach a limit?n=12b. Does the sequence cfw_
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday April 3rd1. Does the series1converge or diverge? Give reasons.nn=1 n + 312. Does the series1converge or diverge? Give reasons.n=0 5n + 323. Does the series1co
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday April 3rd1. Does the series1converge or diverge? Give reasons.nn=1 n + 32. Does the series1converge or diverge? Give reasons.n=0 5n + 33. Does the series1conver
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday April 10th1. Does the series converge or diverge? Give reasons.1n=2 ln n12. Does the series converge or diverge? Give reasons.ln n10n=1 n23. Does the series conve
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday April 10th1. Does the series converge or diverge? Give reasons.1n=2 ln n2. Does the series converge or diverge? Give reasons.ln n10n=1 n3. Does the series converge
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday April 17th1. Find the interval of convergence of the power series.n 2 xnnn=0 212. Find the interval of convergence of the power series.(1)n xnn=0 n + 123. Find th
Delaware - MATH - 242
Math 242, Sections 010 and 011, Spring 2012Suggested discussion problems, Tuesday April 17th1. Find the interval of convergence of the power series.n 2 xnnn=0 22. Find the interval of convergence of the power series.(1)n xnn=0 n + 13. Find the in
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Feb 7th or Feb 9th1. Evaluate the denite integral. /2sin4 x dx012. Find all intersection points of the curves.x2 2y 2 = 27y 2 = 3x23. Evaluate the denite integrals.131
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Feb 7th or Feb 9th1. Evaluate the denite integral. /2sin4 x dx02. Find all intersection points of the curves.x2 2y 2 = 27y 2 = 3x3. Evaluate the denite integrals.13131
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Feb 14th or Feb 16th1a. Find a unit vector that has the same direction as the vector 4, 2, 4 .1b. Find the direction cosines and direction angles of the vector 4, 2, 4 .12. If
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Feb 14th or Feb 16th1a. Find a unit vector that has the same direction as the vector 4, 2, 4 .1b. Find the direction cosines and direction angles of the vector 4, 2, 4 .2. If th
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Feb 21st or Feb 23rd1. Use vectors to decide whether the triangle with vertices P = (1, 3, 2),Q = (2, 0, 4), and R = (6, 2, 5) is right-angled.12. If a vector has direction ang
Delaware - MATH - 243
Math 243, Sections 013 and 015, Spring 2012Suggested discussion problems, Feb 21st or Feb 23rd1. Use vectors to decide whether the triangle with vertices P = (1, 3, 2),Q = (2, 0, 4), and R = (6, 2, 5) is right-angled.2. If a vector has direction angle
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.12. Sketch the region bounded
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