152final2007_2 - 3) perpendicular to plane 3 x + 2 y + z =...

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Last Name Name Student No Department Section Signature : : : : : : : : : : : : : Code Acad.Year Semester Instructors Date Time Duration ATILIM UNIVERSITY Department of Mathematics Calculus II. Final Exam Math 152 2007-2008 Fall A. ¨ O., ¨ U.A., A.D. 07.01.2008 12.30 90 minutes 6 Questions on 4 Pages Total 100 Points 1 2 3 4 5 6 SHOW ALL YOUR YOUR WORK IN DETAILS Question 1 (15 pts.) Find the radius and interval of convergence of the power series X n =1 (2 x - 1) n n + 1
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Question 2 (15 pts.) Let w = 2 ye x - ln z be a function of the variables x,y,z . Evaluate dw dt at t 0 = 1 by using the Chain Rule , where x = ln( t 2 + 1), y = arctan t and z = e t . Question 3 (10 pts.) Find the parametric equations for the line through the point A (1 , 2 ,
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Unformatted text preview: 3) perpendicular to plane 3 x + 2 y + z = 6. Question 4 (15 pts.) Evaluate the double integral Z 3 Z 1 x/ 3 e y 3 dydx . Sketch the integration region. Question 5 (20 pts.) Evaluate the triple integral Z 2 / 2 Z 1-x 2 x Z 1 /x 2-1 /y 2 x 2 y 2 dzdydx by using the Cylindrical Coordinates . Question 6 (7+9+9 pts.) Consider the triple integral Z 2 Z 4-y 2 Z 2-y dzdxdy (a) Sketch the region of integration. (b) Reverse the integration order into dydzdx . (c) Reverse the integration order into dxdydz ....
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This note was uploaded on 11/07/2010 for the course COMPUTER 223-231-25 taught by Professor Mcbulut during the Spring '10 term at A.T. Still University.

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152final2007_2 - 3) perpendicular to plane 3 x + 2 y + z =...

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