MATH 126 Final: MATH 126 UW Final Exam Fall 2015 Solutions
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6. (a) t = 1, t = 1 (b) no. This is parallel to the z-axis if and only if it is a constant multiple of h0, 0, 1i. This would happen only at a value of t such that sin t = cos t = 0 and there is no such t. 4 sin2 t + 9 cos2 t + 1 (d) in nitely many (those values of t such that sin t or cos t is 0) 4 2 (b) (c) y = 2 and y = 1: f (x) = x2 + x3 x4 + 3. 2 x6 + (a) t2(x) = x + x2 (b) one possibility: |f (x) t2(x)| < 1. 6 (uses the bound |f (x)| = 2ex| cos x sin x| < 2ex(2) 4e1/2 < 4 4 = 8 on (cid:2) 1.
