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Unformatted text preview: r ( t ) = (1 + t )ˆ ı + (22 t ) ˆ + 3 ˆ k for 0 ≤ t ≤ 2. [6 pts] Indicate direction. (c) Give a parametrization of the oriented curve shown to the right. [8 pts] This curve is a parabola. For part (c) only. Please put problem 4 on answer sheet 4 4. (a) Given ¯ r ( t ) = 2 t ˆ ı + t 2 ˆ + 1 3 t 3 ˆ k , ±nd ¯ T ( t ). [5 pts] (b) Calculate 1 i 2 t ˆ ı + ( t 21) ˆ + e 2 t ˆ k dt . Simplify. [5 pts] (c) Explain why the parametrization ¯ r ( t ) = ( t 24 t )ˆ ı + 5 ˆ for 0 ≤ t ≤ 3 is piecewise smooth but not smooth. [10 pts] Please put problem 5 on answer sheet 5 5. Find the point on the plane 2 x4 y + z = 10 which is closest to the point (1 , 3 , 0). There is more than one way to do this. Any remotely relevant pictures and/or calculations will be accepted for partial credit. [20 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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