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e210k

# e210k - MAC 2313 Exam II and Key Prof S Hudson 1[10 pts...

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MAC 2313 Oct 14, 2010 Exam II and Key Prof. S. Hudson 1) [10 pts] Convert from spherical to cylindrical coordinates: (5 , π/ 4 , 2 π/ 3). 2) [10 pts] Find the arc length parametrization of the circular helix r = cos t i + sin t j + t k that has reference point r (0) = (1 , 0 , 0) and has the same orientation as the given helix. 3) [10 pts] Find the curvature and radius of curvature for this curve at t = π/ 2. Simplify completely. x = 3 cos t , y = 4 sin t , z = t 4) [10 pts] Determine whether the limit exists. If so, find its value. lim ( x,y ) (0 , 0) xy 3 x 2 + 2 y 2 5) [15 pts] Let f ( x, y, z ) = 2 xy 2 z 3 , P (1 , - 1 , 2) and Q (0 . 99 , - 1 . 02 , 2 . 02). Use a total differ- ential to approximate the change in the value of f from P to Q . Simplify completely. 6) [10 pts] Let f ( x, y ) = xy 2 and u = j . Compute the directional derivative D u f (1 , 1). 7) [15 pts] Answer T or F; you do not have to justify your answers (but this sometimes helps, if there is some minor misunderstanding): For a moving particle, the unit tangent vector and the velocity vector are parallel.

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e210k - MAC 2313 Exam II and Key Prof S Hudson 1[10 pts...

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