Math206Test3

Math206Test3 - Mid-term Exam 3 MthSc 206 – 013 Calculus...

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Unformatted text preview: Mid-term Exam # 3 November 12, 2007 MthSc 206 – 013: Calculus of Several Variables Instruction: PRINT your name clearly in capitals and underline your last name . NAME: EXAM SOLUTION 1. (4pts) For the following circulation motion r ( t ) = h cos 3 t, sin 3 t i . (a) (2pts) Find the unit tangent vector T . Solution: v = d r dt = h- 3 sin 3 t, 3 cos 3 t i | v | = p 9 sin 2 3 t + 9 cos 2 3 t = 3 T = v | v | = h- sin 3 t, cos 3 t i . (b) (2pts) Find the principal unit normal vector N . Solution: From the part (a), we have d T dt = h- 3 cos 3 t,- 3 sin 3 t i ˛ ˛ ˛ d T dt ˛ ˛ ˛ = p 9 cos 2 3 t + 9 sin 2 3 t = 3 , and N = d T dt ˛ ˛ ˛ d T dt ˛ ˛ ˛ = h- cos 3 t,- sin 3 t i . 2. (2pts) Let f ( x, y ) = p x- y 2 . (a) (1pt) Find and sketch the domain of f . Solution: The domain of f is { ( x, y ) : x- y 2 ≥ } . (b) (1pt) Find the range of f . Solution: { z : z ≥ } . 3. (6pts) Find the limit, if exists, or show that the limit does not exist....
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Math206Test3 - Mid-term Exam 3 MthSc 206 – 013 Calculus...

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