Unformatted text preview: quiz 2 solution, math118, 2008 1. (a) limx3 f (x) = 3. (b) limx3 f (x) does not exist. The side limits are dierent:
x3 lim f (x) = 3 = 2 = lim f (x). +
x3 (c) limh0 f (2+h)f (2) = f (2) , slope of the tangent line to the graph of f h through (2, f (2)). From the gure it is immediate that this slope is 0.
Another solution: f (2+h)f (2) h = 33 h f (2) could be computed. Since h 0, = 0, so will be the limit of this when h 0. choose h small, 2. f (x) = x( x + 2) = x3/2 + 2x. f (x) = 3/2x1/2 + 2 (= 3/2 x + 2), f (1) = 3/2+2 = 7/2, f (1) = 1+2 = 3. So the pointslope equation is y3 = 7/2(x1).
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 Fall '07
 Vorel
 Calculus, Derivative, Slope, Limits

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