SECTI In Exercises 19-22, use any method to evaluate the limit or show that it does not exist. 40. lim (x, y ) - (0, 0 lim Boob eolder 20. 10lim Of * 2 - y 2 19. (x, y) - (0,0) Vx2 + 147 grow maistill (x,y)-(0,0) x2+ yz 41. lim xy (x, y ) - (0, 21. lim (x, )')-(0,0) 3x2 + 23/2 22. lim 1 4 - 14 (x, y) - (0,0) x 4 + x 2 2 + 14 42. lim In Exercises 23-24, show that the limit does not exist by approaching the (x, y ) - (1 origin along one or more of the coordinate axes. Hint: Rewr xty tz 23. lim (x, y,2) - (0,0,0) x2 + 2 + z2 24. lim * 2 - 12 + 2 2 43. Let f (x,y,z)-(0,0,0) x2+ y2 + z2 (a) Show 25. Use the Squeeze Theorem to evaluate ow and zoidahav owl to (t.)), nodon 1 lim (x2 - 16) cos pysch li) atmilan (b) Show (x, y)-(4,0) (x -4)2 + 2 (c) Use t (d, 3)) - (dad + 0)T 44. Let 26. Evaluate lim tan x sin (x, y)- (0,0 the limit In Exercises 27-42, evaluate the limit or determine that it does not exist. 10 0 45. Z* COS( It W) 28. lim (zzw -9z) the limi 27. lim ( 2, W ) - (-2, 1) eztu (2,W)-(-1,2) to exist x 2 + 1 2 29. y - 2 lim 30. lim (x,y)- (0,0) 1 + 2 (x, y) - (4,2) ~x2 - 4 xy 31. lim -3 lim 32. (x,y)-(0,0) x2+ 12 (x, y) - (3,4) x2+ 2 cos x sin y 33, COS X lim lim 34. (x,V)- (0,0) (x,y)- (7,0) sin y 1x/ 35. BVID 36. lim lim ex-y In(x - y) (x,y) - (0,0) |x/ + /x/ (x,y)-(1,-3)V 2 - 12 38. lim 37. + 4xy) (x,y) - (2,1) lim (x,y) - (-3,-2) 39. lim tan(x2 + y2) tan -1 * 2 + 1 2 , (x, y) - (0,0) 49 res