Unformatted text preview: z = 0. [6 pts] (b) Sketch the VVF ¯ r ( t ) = 2 t ˆ ı + (24 t ) ˆ + t ˆ k for 0 ≤ t ≤ 2. Indicate direction. [6 pts] (c) Give a parametrization of the oriented semiellipse shown here. [8 pts] Please put problem 4 on answer sheet 4 4. (a) Assuming a and b are positive constants calculate the curvature of the ellipse [10 pts] ¯ r ( t ) = a cos t ˆ ı + b sin t ˆ at t = π 2 . (b) Calculate the length of the curve ¯ r ( t ) = 2 t ˆ ı + t 2 ˆ + ln t ˆ k for 1 ≤ t ≤ 2. Simplify. [10 pts] Please put problem 5 on answer sheet 5 5. (a) Find the position vector satisfying ¯ a ( t ) = 2ˆ ı + 2 ˆ , ¯ v (0) = 1ˆ ı2 ˆ and ¯ r (1) = 3ˆ ı + 5 ˆ . [13 pts] (b) Sketch the plane x + 2 y + 3 z = 12. Label the three intercepts with their coordinates. [7 pts] The End...
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This note was uploaded on 02/27/2012 for the course MATH 2 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff
 Math

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