exam 1 A solutions

exam 1 A solutions - Name: PUID#: Midterm 1A Math 362...

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Name: PUID#: Midterm 1A– Math 362 (2/18/10) SHOW ALL RELEVANT WORK!!! 1. (10pts) Suppose that a particle following the path, c ( t ) = (cos e t , t, 1 - t 2 ), flies off on a tangent at t = 1. The position of the particle at the time t = 3 is (1) (cos e - 2 e 2 sin e 2 , 3 , - 8), (2)(cos e - 3 e 3 sin e 3 , 4 , - 18), (3)(cos e - 2 e sin e, 3 , - 4), (4)(cos e - 3 e sin e, 4 , - 6), and (5)None of the above. solution. (3) The tangent line to the path at t = 1 is l ( t ) = c (1) + ( t - 1) c 0 (1) , where c 0 ( t ) = ( - e t sin( e t ) , 1 , - 2 t ). The position of the particle at the time t = 3 is l (3) = c (1) + (3 - 1) c 0 (1) = (cos e, 1 , 0) + 2( - e sin e, 1 , - 2) = (cos e - 2 e sin e, 3 , - 4) . 2. (10pts) Sketch the curve that is the image of the path c ( t ) = ( | t | , | t + 1 3 | ) where - 1 t 1 . By opening the absolute value, we have c ( t ) = ( - t, - t - 1 / 3) - 1 t ≤ - 1 / 3 , ( - t, t + 1 / 3) - 1 / 3 t 0 , ( t, t + 1 / 3) 0 t 1 . = (0
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This note was uploaded on 05/07/2010 for the course MA 362 taught by Professor Staff during the Spring '08 term at Purdue University.

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exam 1 A solutions - Name: PUID#: Midterm 1A Math 362...

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