Chapter Limits 18. 17. It is false that lim 1000 = 00. Express this fact in a math- * - 00 x ematical sentence involving M and N, to show how the formal definition of limit fails in this case. Skills 48 Write each limit in Exercises 19-42 as a formal statement involving S, E, N, and/or M, and sketch a graph that illus- trates the roles of these constants. In the last six exercises you 49 may take f to be any appropriate graph. x2- 4 19. lim Vx + 7 =2 20. lim = 0 x - -3 x-2 x +2 21. lim (x3 - 2) = -3 22. lim V1 - x = 0 5 X - - 1 x-+1- X - - 4 23. lim = 4 24. lim (x2 - 3) = -2 X- 2x-2 x- 1 25. lim Vx = 0 26. lim (4 - x2) =-5 x - 0+ x -+ 3- 1 27. lim = 0 28. lim - = -00 x- -2+ x + 2 x - 0- X 1 1 29. lim 30. lim x- 2+ 2x - 4 x- 0+ 1 - ex = - 00 X 31. lim = -.5 X-+ 0 1- 2x 32. lim 1 X- -00 x 2 + 1 = 0 33. lim (x3 + x + 1) =00 34. lim (1 - 3x) = 0% X- - 00 (2 + h ) 2- 4 35. lim = 4 h - 0 h 36. lim 2th h - 0 1 37. lim f(x) =-00 h = x -> ct 38. 4 lim f(x) = 00 39. lim f(x) = L x - C X - - 00 40. 41. lim f(x) = 00 lim f ( x) = -00 X- -00 x - -00 42. lim f (x) =-00 For each limit lim f(x) = L in Exer X - 00