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2: Derivatives much as possible. 101-104, you will have to guess the value of the limit us- e of the tangent line m = lim mec(x) ing a computer/calculator and the graphical method (See limit. Find this limit exactly using the Example 2.1.6). (c) Write an equation for the tangent line to f at quation for the tangent line to f at (a, f(a)). Optional: Check your work by graphing the al: Check your work by graphing the function f and the tangent line at the given point. e 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 32. f(x) = 9-12,a = 2 limits. (See Example 2.1.7.) Also in this situation the = 2 34. f(x) =2-13,a=1 tangent line may fail to exist, but tangent lines on each 1=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 38. f(x) = 1/r , a =2 check your work by graphing them and along with f. 40. f(x) = 1/r', a = 1 4 42. f(x) = -1/Vr, a = 9 69. f(x) = 12 - 3x, a =2 70. f(x) = 12 - 4r, a =1 5 71. f(x) = 13 -412 +12, a= 1 ,0 =2 44. f(x) = - 910 =2 x + 3 72. f(x) = 13 -312 +2, a =0 ,0 =2 46. f(I) = 0=1 73. f(x) = Vr+1, a =1 74. f(x) = Vx - 2, a = 5 2+x r+2 75. f(x) = 1/r, a = 2 76. f(x) = 3/r, a = 1 ,a =2 48. f(x) = 1 + 5 77. f(x) = 2/(x +3), a = 2 78. f(x) = 3/(r +2), a = 3 12 , a = 1 50. f(x) = V3+23,a = 2 79. f(x) = 1/x2, a = 2 80. f(x) = 3/x2, a = 1 81. f(x) = 1/x3, a = 2 82. f(x) = 1/x3,a = 1 2,0=2 52. f(x) = 2 2+72:0=1 83. f(x) = 1/Vr, a = 4 84. f(x) = -1/Vr,a =9 2 6 5 3,0=2 54. f(x) = 85. f(x) = - 1610 =2 I + 2 86. f(x) = - -,a =2 r + 3 87. f(x) = -1=2 88. f(x) = 2, 0 = 2 56. f(x) = 2+7210=1 1+r r - 1 1+r 1 - r 58. f(1) = 89. f(x) = 2+2 210 =1 2+ 7 -,1 =2 90. f(x) = -,0=3 2,0 =2 2+ r 92. f(x) = 2 + 3r, a = 1 60. f(x) = Vx2 + 5r,a = 1 91. f(x) = 2+ 210 2 + 1,a =1 62. f(x) = Vx3 + 2,a=1 93. f(x) = 1+2310 =2 94. f(I) = , a = 1 64. f(x) = 2 V9 - 12 a=2 95. f(x) = 96. f(x) = 2+72:0=1 a= 2 66. f(r) =- V4+ 12 97. f(x) = 10 20 =0=1 98. f(I) = 2+ VE VI, a = 1 68. f(x) = \\2+ Vi,a =1 99. f(r) = \\1+ Vz,a =1 100. f(z) = \\2+ Vz,a =1 Calculating Slopes of Tangent Lines 101. f(x) = (10Inx)/x, a = 2 102. f(x) = In(r + 2), a =1 ents h Variable Version) 103. f(x) = re ", a=1 104. f(x) =r'e , a=1 106 , for the given function f and the the following: 105. f(x)= 4-12 if r0 .=0 lee (h) = f(ath) - f(a) h much as possible. of the tangent line lim msec (h) by eval- h-0 NOTE: In Exercises 69-100, find this