写作Math 253编程、辅导Java，c++程序语言

” 写作Math 253编程、辅导Java，c++程序语言Math 253 Final Exam December 2018 Duration: 150 minutesThis test has 8 questions on 8 pages, for a total of 80 points. Read the questions carefully. Where appropriate, give complete arguments and explanations for all your calculations.Answers without proper justification may not be marked. Continue on the closest blank page if you run out of space, and indicate this clearlyon the original page. Attempt to answer all questions for partial credit. This is a closed-book examination. No aids of any kind are allowed, including:notes, cheat Sheets, electronic devices of any kind (including calculators, phones, etc.)First Name: Solutions Last Name:Student-No: Section:Signature:Question: 1 2 3 4 5 6 7 8 TotalPoints: 12 12 9 8 8 8 8 15 80Score:Student Conduct during Examinations1. Each Examination candidate must be prepared to produce,upon the request of the invigilator or examiner, hisor her UBC id card for identification.2. Examination candidates are not permitted to ask questionsof the examiners or invigilators, except in cases ofsupposed Errors or ambiguities in examination questions,illegible or missing material, or the like.3. No examination candidate shall be permitted to enter theexamination room after the expiration of one-half hourfrom the scheduled starting time, or to leave during thefirst half hour of the examination. Should the examinationrun forty-five (45) minutes or less, no examinationcandidate shall be permitted to enter the examinationroom once the examination has begun.4. Examination candidates must conduct themselves honestlyand in accordance with established rules for a givenexamination, which will be articulated by the examiner orinvigilator prior to the examination commencing. Shoulddishonest behaviour be observed by the examiner(s) orinvigilator(s), pleas of accident or forgetfulness shall notbe received.5. Examination candidates suspected of any of the following,or any other similar practices, may be immediately dismissedfrom the Examination by the examiner/invigilator,and may be subject to disciplinary action:i. speaking or communicating with other examinationcandidates, unless otherwise authorized;ii. purposely exposing written papers to the view of otherexamination candidates or imaging devices;iii. purposely viewing the written papers of other examinationcandidates;iv. using or having visible at the place of writing anybooks, papers or other memory aid devices other thanthose authorized by the examiner(s); and,v. using or operating electronic devices including butnot limited to telephones, calculators, computers, orsimilar devices other than those authorized by theexaminer(s)(electronic devices other than those authorizedby the examiner(s) must be completely powereddown if present at the place of writing).6. Examination candidates must not destroy or damage anyexamination material, must hand in all examination papers,and must not take any examination material fromthe examination room without permission of the examineror invigilator.7. Notwithstanding the above, for any mode of examinationthat does not Fall into the traditional, paper-basedmethod, examination candidates shall adhere to any specialrules for conduct as established and articulated bythe examiner.8. Examination candidates must follow any additional examinationrules or directions communicated by the examiner(s)or invigilator(s).Math 253 Final Exam pg 2 of 8 Student-No.12 marks 1. Consider the following contour plot of a function f(x, y). The values of the contours areequally spaced and other reasonable assumptions can be made.1The gradient of f at (9.5, 5.5) is indicated by the black arrow; it is (f)(9.5, 5.5) = h1, 0i.(a) Find the approximate coordinates of the critical points of f on the domain shown.Classify each as a local maximum, a local minimum, a saddle point, or other.Solution: (12, 6) local max (3, 3) local max (6.5, 7.5) local min(7, 4.5) saddle (3.5, 8.5) saddle(b) Find the coordinates of the global maximum of f and the global minimum of f.Solution: (12, 6) is global max, by counting contours. (0, 7.5) is the global min.(c) Is fy(11, 10) negative or positive? (circle the correct answer)Solution: negative: as we move upwards, the contour values are decreasing.(d) Is fyy(11, 10) negative or positive? (circle the correct answer)Solution: Negative: as we move upwards, the contour values are decreasing andthey are also becoming closer togetherthey are decreasing at a faster rate.(e) Suppose f(9.5, 5.5) = 10. Give the approximate value of f(13, 6). Hint: use thegradient to estimate the contour spacing.Solution: First note the magnitude of the gradient is 1. This is a slope = riseover run. Specifically, over a run of 1 we have a rise of 1.1Reasonable assumptions include: the gradient does not vanish along an entire contour; and the functiondoes not fluctuate wildly on a scale smaller that shown by the contours.Page 2Math 253 Final Exam pg 3 of 8 Student-No.Now we look at the diagram. Over a run of 1 (from 9.5 to 10.5) we crossed twocontours. Thus the contour spacing must be 0.5. So f(13, 6) 11.5 (its threecontours above 10).(f) What is the direction of the gradient at the point (6.5, 1)? Circle your answer.(g) An angry fire ant is at (2, 10). It starts walking and with each small step, it movesin the direction of maximum increase of f. On the contour plot above, draw thepath followed by the ant. Hint: practice on the spare rough copy to the left.12 marks 2.2 and consider the implicit surface defined by F(x, y, z) = 0.(a) Find all points on the surface where x = 1 and y = 2Solution: There are two, with z = 2.(b) Let a be a parameter. Consider two planes given bya(x 1) 4(y 2) + 4(z 2) = 0,a(x 1) 4(y 2) 4(z + 2) = 0.What is the Cosine of the angle between their normal vectors?Solution: The normal vectors are u = ha, 4, 4i and v = ha, 4, 4i.(c) Find the value of a such that both planes are tangent to the implicit surface atx = 1 and y = 2. We see thata = 16 (noting the last component matches using our answer from (a)).(d) Set up (but do not evaluate) an integral for the total surface area of the surfacewhere (x, y) is in the rectangular region R = {(x, y) : 0 x 3, 0 y 2}.Solution: Solve for z2 = x4y2. Well need to multiply by 2 because there is atop and bottom to the surface,Math 253 Final Exam pg 4 of 8 Student-No.9 marks 3. In the contour plots below, the values of the contours are evenly spaced. Nine of thesetwelve plots correspond to graphs on the next page.Math 253 Final Exam pg 5 of 8 Student-No.Put the letter of the corresponding contour plot from the previous page in the box beloweach graph. (The axes of the nine graphs below are all oriented in the standard way: thepositive x-axis is on the left, the positive y-axis is on the right, and the positive z-axis isupward.)Math 253 Final Exam pg 6 of 8 Student-No.8 marks 4. Consider the integral Z 8(a) Sketch the domain of integration.Solution: The Domain of integration is the bounded region under the curvey = x3 over the interval 0 x 2.(b) Evaluate the integral.Solution: We cannot find a closed form for the antiderivative of ex4, so ourstrategy is to switch the order of integration. Upon switching the order ofintegration,(b) Indicate whether each statement about a lamina is true or false (circle your answer).i. True/ False : If (x, y) = 0, then the mass is independent of 0.ii. True /False: If (x, y) = 0, then the centre of mass is independent of 0.iii. True/ False : If (x, y) = f(x) then y = 0 (because y is an odd function).(c) Sketch a shape D of uniform density whose centre of mass is not contained in D.Solution: Lots of Non-convex shapes have this property, an annulus or part ofan annulus for Example.3. Fill in the boxes below to complete the integrals for the volume of C.如有需要，请加QQ：99515681 或邮箱：99515681@qq.com

“