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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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 Spring '07
 Smith
 Math, student ID number, following polar curve

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