Math 126C Second Midterm Winter 2009 Your Name Your Signature Student ID # Luke Chris Section 11:30 12:30 11:30 12:30 (circle one) CA CB CC CD Problem Total Points Score 1 8 2 6 3 14 4 12 5 10 Total 50 This exam is closed book. You may use one 812 11 sheet of notes. Graphing calculators are not allowed. In order to receive credit, you must show your work. Explain why your answers are correct. If you use a trial and error (or guess and check) method when a calculus method is available, you will not receive full credit. Place a box around YOUR FINAL ANSWER to each question. If you need more room, use the backs of the pages and indicate to the reader that you have done so. Raise your hand if you have a question. Math 126C Second Midterm Winter 2009 1 (8 points) Let r(t) = (2t 1)i+t2 j+2ptk. Find all times t when the tangential component of acceleration is zero. 2 (6 points) Find the equation of the tangent plane of the function F(x; y) = 3y 25x + 7 at the point ( 1; 1). Math 126C Second Midterm Winter 2009 3 (14 points) Evaluate the following double integrals. (a) (7 points) ZZ R xy sin(x2y) dA; R = [0; 1] [0; =2] (b) (7 points) ZZ D y2exy dA; D = f (x; y) j 0 y 3; 0 x y g Math 126C Second Midterm Winter 2009 4 (12 points) You wish to build a rectangular box with no top with volume 6 ft3. The material for the bottom is metal and costs $3.00 a square foot. The sides are wooden and cost $2.00 a square foot. Calculate the dimesnsions of the box with minimum cost. Use the Second Derivative test to verify that your answer is indeed a minimum. Math 126C Second Midterm Winter 2009 5 (10 points) A table of values is given for a function g(x; y) de ned on R = [0; 1] [1; 4]. (For example, g(1; 4) = 9:4.) Use the table to nd a linear approximation to g(x; y) near (0:5; 3). Use it to approximate g(0:6; 2:8). Carefully explain all your reasoning. 1 1.5 2 2.5 3 3.5 4 0 1 1.8 2.8 3.9 5.2 6.5 8.0 0.25 1.2 1.9 2.9 4.0 5.3 6.6 8.2 0.5 1.4 2.1 3.1 4.2 5.5 6.8 8.5 0.75 1.6 2.2 3.3 4.5 5.8 7.0 8.9 1 1.7 2.3 3.6 4.8 6.1 7.3 9.4
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