804 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES Exercises In Exercises 1-6, at each point evaluate the function or indicate that the function is undefined there. 1. f (x, y ) = x+ yx3, (1, 2), (-1, 6), (e, it) 2. 8 (x, V) = 72 _ 2' (1, 3), (3, -3), ( V2, 2) 3. h(x, y ) = V Vx - y2 (20, 2), (1, -2), (1, 1) X - 4. k(x, y) = xe-", (1, 0), (3, -3), (0, 12) 5. h(x, y, z) = xyz-2, (3, 7, - 2), (3, 2, 4 ), (4, -4, 0) 6. w(r, s, 1 ) = -s 21 sin t ( 2, 2, E ), ( JE , JE , JE ) , ( - 2, 2, 6 ) (a) (b In Exercises 7-14, sketch the domain of the function. (c 7. f(x, y) = 12x - 5y 8. f (x, y ) = V81 -x2 9. f(x, y) = In(4x2 - y) boonto 10. h(x, t) = x t t 11. 8(), z) = - 1 12. f (x, y) = sin = 13. F(I, R) = VIR 14. f(x, y) = cos-(x + y) In Exercises 15-18, describe the domain and range of the function. 15 . f ( x , y , Z ) = xz+ ey 16. f ( x, y , z ) = x Vy + ze?/x 17. P(r, s, t) = 16-252+2 18. g(r, s) = cos-(rs) 19. Match graphs (A) and (B) in Figure 18 with the functions. (i) f(x, y ) = -x+yz (ii) 8 (x, y) = x+ yz ordi e (A) (B) FIGURE 18 ba 20. Match each of graphs (A) and (B) in Figure 19 with one of the follow- ing functions: () f(x, y) = (cos x)(cos y) (ii) 8(x, y) = cos(x2 + y2)BLES the (B) (A) FIGURE 19 21. Match the functions (a)-(f) with their graphs (A)-(F) in Figure 20. (a) f(x, y ) = 1x1+ 1yl (b) f (x, y) = cos(x - y) ( c) f ( x, y ) = = - 1 1 + 9x2 + 12 (d) f (x, y) = cos(y3 )e-0.1(12+32) -1 (e) f(x, y ) = 1+ 9x2 +92 (f) f (x, y) = cos(x2+ 3)e-0.1(x2+12) (A) (B) -N svat offi lo guide Strand of 9 moil (C) N (E) a lo as we love (F) FIGURE 20