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Sophie Chrysostomou

University of Toronto at Scarborough Department of Computer & Mathematical Sciences MAT A30Y 2012-2013 Assignment #1 You are expected to work on this assignment prior to your tutorial during the week of September 16th. You may ask questions about this assignment in that tutorial. In your tutorial during the week of September 23re you will be asked to write a quiz based on this assignment and/or related material from the lectures and textbook readings. TEXTBOOK: Single Variable Calculus, Early Transcendentals, 7e, J.Stewart READ: Stewart: Sections: 1.1, 1.2. Notes: 1 Functions pages 8-14. . Calculus Review Manual (CRM) pages 6-11. PROBLEMS: A. Homework problems from the lectures: 1. Show that: (i) the product of two even functions is an even function. (ii) the product of two odd functions is an even function. (iii) the product or an odd and an even function is an odd function. 2. Use the factor theorem to show that 4 3 2 (a) x − 2x + 4x − 5x − 6 is divisible by x − 2. 5 4 3 2 2 (b) x + 4x + 2x − 2x + x − 6 is divisible by x + 2x − 3. 3 2 (c) x + (2 − a)x + (5 − 2a)x − 5a is divisible by x − a. 3. Use the rational root theorem to find if p(x) = x + 8x + 19x + 22x + 10 has any rational roots. If there are such roots factor p(x) as far as possible. P(x) R(x) 4. For the following functions f(x) =D(x) express f(x) in the form f(x) = Q(x)+ D(x) , where the deg(R) < deg(D). 2 2 i) f(x) = x ii) f(x) = x + 1 x − 1 x − 2 3 3 iii) f(x) = x iv) f(x) = x − b x − 2 x + a 3 3 v) f(x) = x − 3 vi) vi) f(x) = x − 1 x + x + 1 x + x + 1 B. WebAssign or Book Problems. WebAssign. For students who have chosen method of evaluation option A: There are 3 parts to
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