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MAT290H1F_FinalExam_2009

# Cos 2 marks 3 a show that for we can write and 6

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Unformatted text preview: hat for , we can write: and (6 marks) b) Given the function 2 1 1 express this as a function of , where Page 6 of 17 . (8 marks) 3. c) For the function , evaluate the integral 2 Page 7 of 17 (4 marks) 3. d) Prove that cosh cosh cos sinh sin Page 8 of 17 (8 marks) 4. a) Suppose the function Does is analytic for | | 2, and 1 5 cos 3 4 sin 0 have any solutions in the unit disc | | Page 9 of 17 0 1? 2 4. b) For the function what are the values of the following integrals? Explain your answers with sound mathematical reasoning and/or calculations. State the name of any theorems that you use in your explanations. defined by | | (2 marks) (i) For , travelled in the counterclockwise direction. (3 marks) (ii) For being a triangle with vertices of the counterclockwise direction. (3 marks) (iii) For being an L-shaped path starting from ending at 2 3. 3 Page 10 of 17 1, 1, and 1, moving to 4 , travelled in 2, and then 4. b) (cont’d) (4 marks) y 4 3 (iv) For being the path shown to the right. This path starts at 4 , then travels through the origin to 4 , then...
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