MATH 126 Final: MATH 126 UW Final Exam Spring 07 Solutions
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1. (a) answer: t2(x) = 2 + 4(x 1) + 3(x 1)2 (b) hint: taylor"s inequality states that the error is bounded by. |x 1|3, where m is an upper bound of f (x) on the interval j. But f (x) = 6 for all values of x. So, we can take m to be 6 and we need an interval j on which |x 1|3 < 0. 001. 3: hint: the taylor series for ex2. Answer: the taylor series for f (x) is. 3 + 7x + 9x2 + 12. 5x3 + : (a) f; (b) t; (c) f; (d) t; (e) f; (f) t; (g) t; (h) f. 4. (a) answer: x = 1, y = t, z = 3 + t (b) answer: 5x 2y + 2z = 1: answer: 1. 7 (x 2) + 2 (b) answer: the curve has a horizontal tangent at t = 1.
