MATH 126 Final: MATH 126 UW Final Exam Winter 2014 Solutions
Document Summary
Winter 2014: (a) t; (b) f; (c) f; (d) f; (e) f; (f) f; (g) f; (h) f. 2 , 9 (a) 5 2 (b) (cid:0) 9. 2 , 3 (a) 2x y + z = 0 (b) x = 2 + t, y = 4 + 4t, z = 2t. 2 , (cid:1) mum at (cid:0) f(cid:0)x, . 2(cid:1) = 0, where x is any value in the interval 0 x (a) fx(x, y) = yxy 1 + ln(y)yx, fy(x, y) = ln(x)xy + xyx 1. 2 , 0(cid:1) = 1 and the absolute minimum is. 7. (b) z = x + y (c) f (1. 01, 0. 99) 2 (a) z = x (b) the line y = x: 0, 9. (a) hint: note that f (x) = ln(x2 + 3x) = ln(x) + ln(x + 3). Xk=1 (b) taylor series for f (x): ln(4)(x 1) + (c) k. 4k(cid:1) ( 1)k+1(cid:0)1 + 1 k(k + 1) (x 1)k+1.
