Advanced Calculus fi..

) z= 1,x = ~,y =O;e) ylx + xly - z = x ~y~;c) 2x-y -z=0,9 = 5 = %; d) none;f) (yi + z~)x + (XI + ZI)Y + (XI + YI)Z = 2.10. a) z-2=2(x - 1)+2(y - 11, + = Y_?_1 = q;b) z- $ = -2(x- $) -2(y - $), = 912 z-L= +;c) z=x-2y+2,x=2+t,y=1-2t,z=2-t;4 8d) 5 ~=6~+8y-lO,x=$+gt,y=~+jt,z=-t.11. a) x=3+4t,y=1-5t,z=1+3t; b) x=2+t,y=2-t,z=l;c) x = I , =-l+t,z=-t.~Answers to Problems 71 9=+4k.de~fllSection 2.14, page 1341. a) - b) 0; c) ; d) -5; e -4; f) 0. 2. a) x2 - Y'; 97xyz6. dulds = -2xy. Minimum is -4 at (0, f 2).b, ,/x2 +4y2 + L6z2.8. Maximum is 6 in direction i at (1, 0), in direction -i at (-1,O). 9. 3, 1 l543' 33'Section 2.18. wee 142 1.Section 2.21, page 1581. a) maw. at -1, min. at 1; b) max. at n/3 + 2nn, min. at -n/3 + 2nn, horiz. infl. atn + 2nn (n = 0, f 1, f 2, ...); c) max. at log 2.2. min. for n = 2,4,6, ..., horiz. infl. for n = 3,5,7, ....3. a) max.=l,min.=O; b) max.=O; c) nomax.ormin.;1d) maw. = 2, min. = -2. 1 4. a) max. at (0,O); b) min. at (0,O);c) saddle point at (1, 1); d) saddle point at (0,O); e) critical point at every point of theline y = x, each point giving a relative min.; f) triple saddle point at (0,O); . , ,,,g) min. at (A,2 + 2nn), (-&, 9 + 2nn), neither at (0, nn. - 2);h) min. at (4, 3). saddle points at (0, O), (1, O), (0, 1); i) (0,j) min. at (0,O); k) min. at (0, f I), saddle point at (0,O).5. a) abs. max. at (0,O); b) saddle point at (0,O);:! ,0), neither max. nor min.;