ANSWERS TO DAVID ESSNER EXAM II, 1982-93

(a) f(x) = x(3x – 1)/(2x – 1). To make f(x) > 0 a given x must lie between 0 and 1/3 or be > 1/2 (b) Use the identity cos 2A = 2 cos2A – 1 with A = 22 1/2 . Then /2 = cos 45 = 2 cos2 22 1/2 - 1 = 2(x/2)2 - 1 where x is the length of the other side. (d) This is the intersection of the circle (x – 2)2 + y2 = 1 and the ellipse (x – 1)2… ................
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