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# a7 - 3 Section 12.5 Page 552 553 2 4 7 8 11 16 22 25 28 4...

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University of Toronto at Scarborough Department of Computer & Mathematical Sciences MATA32 Assignment 7 Fall 2009 Be prepared to ask questions and receive instruction about this assignment in the 7th tutorial, which takes place during the week of Thursday, October 29 - Wednesday, November 4. Remember: there is a quiz on assignment 6 in the 7th tutorial. Quiz 7 is based on this assignment 7 (or can even contain questions from material pertaining to assignment 6), the relevant text readings for assignments 6 and 7, and similar lecture notes. Quiz 7 will be written by all students in the 8th tutorial, which takes place during the week Thursday, November 5 - Wednesday, November 11 Study: Sections 12.3 - 12.7 and 13.1 for this assignment. Read ahead in sections 13.2 - 13.6 for future lectures and assignments. Problems: 1. Section 12.3, Page 544 # 26, 28, 29. 2. Section 12.4, Pages 548 - 549 # 3 - 6, 12 - 14, 18 - 21, 25, 26, 29, 30, 39, 40. 3. Section 12.5, Page 552 - 553
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Unformatted text preview: 3. Section 12.5, Page 552 - 553 # 2 - 4, 7, 8, 11 - 16, 22 - 25, 28. 4. Section 12.7, Pages 560 # 4 - 8, 11, 12, 15, 17 - 19, 23, 26 - 28, 31, 32, 34. 5. Section 13.1, Pages 576 - 578 # 1 - 3, 5, 6, 9, 10, 13, 14, 16. 6. If the equation xy + y 2 = 2 x deﬁnes y implicitly as a function of x , verify that y 00 =-8 ( x + 2 y ) 3 7. Find all values of the Greek letter λ (pronounced ”lambda”) for which the function y = e λx is a solution to the equation y 00 + y-2 y = 0. What happens if you re-work the problem for the equation y 00 + y + 2 y = 0 ? 8. Find the ”formula” for the function H ( n ) = f ( n ) (1) where f ( x ) = e-2 x and n is a natural number. 9. Find y where (a) x y = y x (b) y = x a e kx-c where a,c and k are constants. 10. Find the cubic polynomial Q for which Q (1) = 1, Q (1) = 3, Q 00 (1) = 6 and Q 000 (1) = 12. 11. Section 12.6, Page 556 # 1 - 3, 9 - 16....
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