exam1_math2500

# exam1_math2500 - ~ r t =(cos 3 t sin 3 t on the interval...

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MATH 2550 Midterm Exam September 22, 2006 NAME (please print legibly): Please complete all 5 questions in the space provided. You may use the backs of the pages for extra space, or ask me for more paper if needed. Work carefully, and try to complete the problems you ﬁnd easier before going back to the harder ones. Good luck! QUESTION VALUE SCORE 1 10 2 10 3 10 4 10 5 10 TOTAL 50 1

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1. (10 points) Find an equation for the plane through the points (2 , 4 , 1) , (0 , 0 , 1) and (0 , 0 , 7) in the form ax + by + cz = d . ANSWER: 2. (10 points) Find the unit tangent vector to the curve ~ r ( t ) = (sin t, 3 t 2 , ln t ) at the point t = π . If your answer is not a unit vector, you will lose points on this question. ANSWER: 2
3. ( 10 points) Find the arclength of the curve

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Unformatted text preview: ~ r ( t ) = (cos 3 t, sin 3 t ) on the interval ≤ t ≤ π/ 2 . ANSWER: 3 4. (10 points) A racecar driver drives on a mountain road. Her position function is ~ r ( t ) = (cos t, 2 sin t ) . The height of the mountain is given by the function h ( x, y ) = x 2-2 xy + 3 y 2 . Find the rate of change of her elevation at a function of t . Hint: We are computing d dt h ( ~ r ( t )) . ANSWER: 4 5. (10 points) Sketch the level curves of the function shown below. Use the x and y coordinate values shown on the sides of the plot to help you ﬁgure out the shape of the curves. 5...
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exam1_math2500 - ~ r t =(cos 3 t sin 3 t on the interval...

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