MATH 320 Midterm: MATH 320 2007 Winter Test 1
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Instructions: the total time is 2 hours and 30 minutes, the total score is 100 points, use the reverse side of each page if you need extra space, show all your work. A correct answer without intermediate steps will receive no credit: calculators and cheat sheets are not allowed. Uniformly continuous? (3 points) (b) show that for every x m , the sequence of functional iterates (5 points) {f (n)(x) : n n} is a cauchy sequence. P = nx = (x1, x2, ) : 1 n for all n no (10 points) 6: (a) describe the closure of the set. 8 (c) repeat the question in part (b) for the closure of the set. F = n(cid:16)x, arctan(cid:16) 1 x2(cid:17)(cid:17) : 0 < x 1o. (5 points: (a) recall the hilbert cube. H = {x = (x1, x2, ) : |xn| 1 for all n n} with metric d(x, y) =
