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74 Chapter 2: Derivatives and simplify as much as possible. 101-104, you will have to guess the value of the limit us- (b) Find the slope of the tangent line m = lim msec(r) ing a computer/calculator and the graphical method (See by evaluating the limit. Find this limit exactly using the Example 2.1.6). algebraic method, (c) Write an equation for the tangent line to f at (c) Write an equation for the tangent line to f at (a, f(a)). Optional: Check your work by graphing the (a, f(a)). Optional: Check your work by graphing the function f and the tangent line at the given point. function f and the tangent line at the given point. NOTE: In 105-106, the function f is piecewise-defined, so in evaluating the limit, you will have to use one-sided 31. f(x) =4-12,a = 1 32. f(x) =9-x2,a = 2 limits. (See Example 2.1.7.) Also in this situation the 33. f(x) =1-13,a =2 34. f(x) =2-13,a=1 tangent line may fail to exist, but tangent lines on each 35. f(x) = 1/x, a = 2 36. f(x) = 2/r, a = 1 side of where the graph is pieced together may exist. If so, for part (c) write equations for these two lines and 37. f(x) = 1/z,a = 3 38. f(x) = 1/12, a = 2 check your work by graphing them and along with f. 39. f(x) = 1/23,a = 2 40. f(x) = 1/x3, a =1 41. f(x) = 1/Vx, a = 4 42. f(x) = -1/Vr, a = 9 69. f(x) = 12 - 3x, a =2 70. f(x) = 12 - 4r, a =1 71. f(x) = 13 -4x2 +12, a= 1 43. f(x) = - 6 10 =2 5 r + 2 44. f(x) = - ,a =2 1 +3 72. f(x) = 3 -312 +2, a =0 45. f(x) = ,0=2 46. f(x) = 73. f(x) = Vr+1, a =1 74. f(x) = Vx -2, a =5 1+ 1 2+1 47. f(x) = a + 1 48. f(x) = 2+ 2 75. f(x) = 1/r, a = 2 76. f(x) = 3/r, a = 1 7 + 3 a=1 2 +5 77. f(x) = 2/(x +3), a = 2 78. f(x) = 3/(x+ 2), a = 3 49. f(x) = \\5+12,a =1 50. f(x) = \\3+12,a = 2 79. f(x) = 1/x, a = 2 80. f(x) = 3/r2, a =1 81. f(x) = 1/r3, a = 2 82. f(x) = 1/x3,a=1 51. f(x) = 2 1+ 7210 =2 52. f(x) = 83. f(r) = 1/VI, a = 4 84. f(x) = -1/VI,a = 9 1 2 53. f(r) = . 1473,0=2 54. f(x) = 1=1 85. f(x) = -,a=2 86. f(x) = = 2 87. f(x) = ,1 =2 88. f(x) = 55. f(x) = 1+ 7210=2 56. f(I) = 2+ 2' 210 =1 1+r x- 1 1+r 1- I 89. f(x) = 90. f(r) = 57. f(x) = 147210=2 58. f(:) = ,4 24=1 59. f(x) = vz? + 3x, a = 160. f(x) = Vx2 +5r,a = 1 91. f(x) = 1+ 7210 =2 92. f(x) = 2 2+72:0=1 2 61. f(x) = Vx3 +1,a =1 62. f(x) = Vx3 +2,a=1 93. f(x) = 1 94. f(x) = 63. f(x) = , a = 1 64. f(x) = - V9 -1 =,a=2 95. f(x) = 1+210=2 96. f(x) = 65. f(x) = - VI+ 0=2 66. f(x) = V4 + x2 97. f(x) = - 10 20 1 + 98. f(x) = 2+ VI 2 0 =1 67. f(x) = \\1+ Vz,a= 1 68. f(x) = \\2+ Vi,a=1 99. f(x) = \\1+ vz,a=1 100. f(z) = \\2+ Vz,a =1 Algebraically Calculating Slopes of Tangent Lines 101. f(x) = (10Inz)/x, a = 2 102. f(x) = In(x + 2), a =1 (Newton Quotients h Variable Version) 103. f(x) = re , a=1 104. f(x) =re , a=1 In Exercises 69-106 , for the given function f and the given point a, do the following: 105. f(2) = 4-12 if r
