1322_midterm2_2004 - Mat 1322D Calculus 2 Professor Arian...

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Mat 1322D, Calculus 2 November 3rd, 2004 Professor. Arian Novruzi Lastname, Firstname: Department of Mathematics Student number: email: [email protected] tel: (613) 562 5800 x 3530 MIDTERM 2 (time 80 min) Notes 1) No books or any other document are allowed 2) A simple calculator with no programming and graphical capabilities can be used 3) Solve each problem using the space following it; if more space is needed use the back of any page or additional white pages after Problem 7 and indicate when doing so 4) Students may not enter after or leave before 20 minutes from beginning of the midterm 5) Students must present their student cards if asked 6) Any question concerning marks or marking must be submitted to the professor within one week after the midterms have been returned Problem Points You 1 5 2 4 3 6 4 5 5 5 6 5 Total 30
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Problem 1 ( § 7 . 2 / 11 - 14) a) Fill the following table with y 0 ( x ) = x + y + 1 for x = - 3 , - 1 , 0 , 1 , 2, and y = - 2 , - 1 , 0 , 1 , 2 , 3. b) Sketch the direction field of the differential equation y 0 = x + y + 1. c) Using the initial condition y (0) = 0 sketch the solution y = y ( x ) for x [ - 3 , 2]. Solution a) y \ x -3 -2 -1 0 1 2 3 1 2 3 4 5 6 2 0 1 2 3 4 5 1 -1 0 1 2 3 4 0 -2 -1 0 1 2 3 -1 -3 -2 -1 0 1 2 -2 -4 -3 -2 -1 0 1 Figure 1: The values of y 0 ( x ) = x + y + 1
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