# mid2v - 1 3 5 1 3 5 x y 2(10 points Consider the curve r =...

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Midterm 2 May 10, 2007 Name: Student ID Number: 1 10 2 10 3 10 4 15 5 15 Total 60 You are allowed to use a scientiﬁc calculator only (no graphing calculators) and one, hand- written , double-sided page of notes. Check that your exam contains all the problems listed above. You must show your work on all problems. The correct answer with no supporting work may result in no credit. If you need more room, use the backs of the pages and indicate to the grader that you have done so. Leave answers in exact form. Remember to check your work.

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1. (10 points) Plot the following polar curve for 0 θ < 2 π r = 1 + 2 θ π . Make sure that the intersection of the axes are correct and well labeled.

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Unformatted text preview: 1 3 5 1 3 5 x y 2. (10 points) Consider the curve r = h t + 2 t 3 , t + e t i . (a) Find parametric equations for the tangent line at (0 , 1). (b) Find all t such that the tangent line is vertical. 3. (10 points) Consider the curve r = h t, t 2 , 1 3 t 3 i . Find the unit tangent T and the unit normal N at the point (0 , , 0). 4. (15 points) Consider the curve r = h 4 t, 3 cos( t ) , 3 sin( t ) i . for 0 ≤ t ≤ 2 π . Find: (a) (5pts) its length (b) (10pts) its curvature 5. (15 points) Let z = f ( x, y ) = q e x /y . (a) Find the domain of f (b) Calculate f x , f y and f xy (c) Sketch the level curves for z = 1 and z = 2...
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mid2v - 1 3 5 1 3 5 x y 2(10 points Consider the curve r =...

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