MATH 13 Study Guide - Final Guide: Xu
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Total marks = 100 (per question in brackets) Unless otherwise stated, include all your working for full credit. Try all parts of every question, even if you can"t do the rst part! A = {x r : 0 x 20} B = {n n : n < 21} D = {n n : n is divisible by 3} Justify your answer. (10) (4) (3: prove by induction: n . 1 k(k + 1) k=2 n 1. 2(n + 1) (10) (a) use the fact that (2x + y)2 0 for all real numbers x, y to prove that. 5x2 + y2 + 4xy + 1 2x (b) suppose that x, y r satisfy 5x2 + y2 + 4xy + 1 = 2x. What are x and y? (4: let x = [0, 1] q be the set of rational numbers between 0 and 1. (a) state injective functions f. : n x and g : x q.
