Exam 1 b solutions - Name PUID Midterm 1B Math 362 SHOW ALL RELEVANT WORK 1(10pts Suppose that a particle following the path c(t =(cos2 t 3t t3 1/t

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Name: PUID#: Midterm 1B– Math 362 (2/18/10) SHOW ALL RELEVANT WORK!!! 1. (10pts) Suppose that a particle following the path, c ( t ) = (cos 2 t, 3 t - t 3 , 1 /t ), flies off on a tangent at t = 1. The position of the particle at the time t = 2 is (1) (cos 2 1 - 2sin 2 , 2 , - 1), (2) (2 cos 2 1 - sin2 , 4 , 1), (3) (cos 2 1 - cos2 , 2 , 0), (4) (cos 2 1 - sin2 , 2 , 0), and (5) None of the above. solution. (4) The tangent line to the path at t = 1 is l ( t ) = c (1) + ( t - 1) c 0 (1) , where c 0 ( t ) = ( - 2sin(2 t ) , 3 - 3 t 2 , - t - 2 ). The position of the particle at the time t = 2 is l (3) = c (1) + (2 - 1) c 0 (1) = (cos 2 1 , 2 , 1) + ( - sin2 , 0 , - 1) = (cos 2 1 - sin2 , 2 , 0) . 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 , - 1 / 3) + t ( - 1 , - 1) - 1 t ≤ - 1 / 3 , (0 , 1 / 3) + t ( - 1 , 1) - 1 / 3
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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-West Lafayette.

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Exam 1 b solutions - Name PUID Midterm 1B Math 362 SHOW ALL RELEVANT WORK 1(10pts Suppose that a particle following the path c(t =(cos2 t 3t t3 1/t

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