MATA32H3 Quiz: MATA32H3 Quiz 6 2010 Winter Solution
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MATA32H3 Full Course Notes
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Key: the picture below shows a graph of y = f (x). If so, evaluate it; if not, explain why not. As indicated in the picture, f ( 1) = 1. 1 from the left, the value of f (x) is approaching 2; in other f (x) = 2. Since the left words, f (x) = 2. Similarly, lim x 1 lim x 1+ and right limits both exist and agree, we conclude that lim x 1 f (x) exists, and equals 2. Continued on reverse: (a) consider lim x 2 explain why not. x + 2 x2. First, note that this is a 0/0 case, which means the answer could be anything so we have to work out the answer carefully. Here we go: lim x 2 x + 2. 4 x2 x + 2 (x + 2)(x 2) 4 (b) consider lim x 2 explain why not. x + 2.