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Exam 2 November 23 2015 MTH 234 Name Section Recitation Instructor READ THE FOLLOWING INSTRUCTIONS Do not open your exam until told to do so No calculators cell phones or any other electronic devices can be used on this exam Clear your desk of everything excepts pens pencils and erasers If you need scratch paper use the back of the previous page Without fully opening the exam check that you have pages 1 through 9 Fill in your name etc on this rst page Show all your work Write your answers clearly Include enough steps for the grader to be able to follow your work Don t skip limits or equal signs etc Include words to clarify your reasoning Do rst all of the problems you know how to do immediately Do not spend too much time on any particular problem Return to di cult problems later If you have any questions please raise your hand and a proctor will come to you There is no talking allowed during the exam You will be given exactly 90 minutes for this exam I have read and understand the above instructions SIGNATURE Page 1 of 9 MTH 234 Exam 2 November 23 2015 Multiple Choice Circle the best answer No work needed No partial credit available 1 5 points Parameterize the part of the plane 6x 3y z 12 that lies in the rst octant A r s t B r s t C r s t 6s 3t 12 h s t 12 h s t 12 h s t 12 h 6s s 6s t i 3t i s t i with s 3t with s 0 2 and t 0 2 and t 0 4 2s 0 4 2s i with s 0 2 and t with s 0 2 and t 0 4 0 4 D r s t E None of the above 2 5 points Which of the following vector eld plots could be F xy i y2 j A B C D Extra Work Space Page 2 of 9 MTH 234 Exam 2 November 23 2015 3 5 points Let F cid 10 x2 xy 3z cid 11 Which of the following is true A curl F y and div F 3x 3 B curl F y and div F 2x x 3 C curl F D curl F 0 0 y i 2x x 3 h h i E None of the above h i and div F 3x 3 and div F y Fill in the Blanks No work needed No partial credit available 4 5 points Write the spherical equation cos in rectangular coordinates 5 10 points Convert the integral 1 1 y2 x 2 x 0 1 0 2 y dz dx dy to an equivalent integral in cylindrical coordinates 2 r2 z2 1 0 0 dz dr d where 1 2 r2 z2 Extra Work Space Page 3 of 9 MTH 234 Exam 2 November 23 2015 Standard Response Questions Show all work to receive credit Please BOX your nal answer 6 10 points Let f x y z x ex yz2 f at P0 0 2 a Find 3 b Find the derivative of f at P0 in the direction of the vector A 2 i j 2 k 7 14 points Let f x y x3 12xy 8y3 Find and classify each critical point of f as a local minimum a local maximum or a saddle point Page 4 of 9 MTH 234 Exam 2 November 23 2015 8 12 points Sketch the region of integration for the integral below and evaluate the integral by reversing the order of integration 1 1 0 y 2 sin x dx dy 9 12 points Evaluate the integral below 2 4 x2 0 4 x2 1 p1 x2 y2 dy dx Page 5 of 9 MTH 234 November 23 2015 10 12 points Find the volume of the part of the sphere 2 that lies between the cones 4 and 3 Exam 2 11 12 points Find the area of the surface z xy that lies inside the cylinder x2 y2 4 Page 6 of 9 MTH 234 12 12 points Find the work done by the force F 4y 2x along the straight line segment from 2 8 to 1 2 Exam 2 h i November 23 2015 13 Let F 2 2xyez i x2ez j x2yez k and answer the questions below a 6 points Find a function f so that f F b 6 points Let C be any path from 2 1 0 to 3 0 1 Evaluate the integral 2 2xyez dx x ez dy x yez dz 2 2 C Page 7 of 9 MTH 234 Exam 2 November 23 2015 14 14 points Let E x y z iterated integral and evaluate 1 y 4 y z 4 0 x z Rewrite the triple integral below as an z x2 z2 dV E 15 10 points Use Green s Theorem to evaluate the line integral dr Here C is the circle x2 y2 4 positively oriented and F C F x y 3y cos y x sin y h i Page 8 of 9 MTH 234 Exam 2 November 23 2015 Congratulations you are now done with the exam Go back and check your solutions for accuracy and clarity Make sure your nal answers are BOXED When you are completely happy with your work please bring your exam to the front to be handed in Please have your MSU student ID ready so that is can be checked DO NOT WRITE BELOW THIS LINE Page Points Score 2 3 4 5 6 7 8 10 20 24 24 24 24 24 Total 150 Page 9 of 9

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