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Practice Final, Spring 2013, Cheat Sheet.
Typology: Exams
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Circle one: Section 6 Section 7.
Question: 1 2 3 4 5 6 7 8 9 10 Total Points: 10 10 10 10 10 10 10 10 10 10 100 Score:
(a) The curve traced by 〈cos^2 (t), sin^2 (t)〉 is a circle. True False
(b) The plane 3x + 2y − z = 0 is perpendicular to the line x = 3t, y = 2t, z = −t. True False
(c) The function f (x, y, z) =
{sin(x+y+z) x+y+z if^ x^ +^ y^ +^ z^6 = 0 1 if x + y + z = 0 is continuous at (0, 0 , 0). True False
(d) If the acceleration is constant, then the trajectory must be a straight line. True False
(e) The complex number e2+3i^ has magnitude 2. True False
(a) (3 points) Mark any three critical points of f. Label them A, B, and C. Identify whether they are local minima, local maxima or saddle points.
(b) (2 points) Draw a vector at (1, 1) indicating the direction of ∇f at (1, 1). (c) (3 points) Determine the sign of
(b) (5 points) Write an equation of the normal plane to the curve at the same point.
(b) (3 points) Where is the ball when it hits the ground?
(a) (2 points) Find the value of u when s = 2 and t = 2.
(b) (8 points) Find an approximate numerical value of u when s = 2.01 and t = 1.98.
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