Only #70

101-104, you will have to guess the value of the limit us- ing a computer/calculator and the graphical method (See Example 2.1.6). (c) Write an equation for the tangent line to f at (a, f(a)). Optional: Check your work by graphing the 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 limits. (See Example 2.1.7.) Also in this situation the tangent line may fail to exist, but tangent lines on each side of where the graph is pieced together may exist. If so, for part (c) write equations for these two lines and check your work by graphing them and along with f. 69. f(x) = x2 - 3x, a = 2 70. f(x) = x2 - 4x, a =1 71. f(x) = 13 -4x2 +12, a = 1 72. f(x) = 13 -312 +2, a=0 73. f(x) = Vr+1, a =1 74. f(x) = Vx - 2, a = 5 75. f(x) = 1/r, a = 2 76. f(x) = 3/r, a = 1 77. f(x) = 2/(x +3), a =2 78. f(x) = 3/(r+2), a = 3 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 83. f(x) = 1/Vr,a = 4 84. f(x) = -1/ V., a =9 85. f(x) = - 6 -,a=2 86. f(x) = 5 x + 2' 1 + 3 , a =2 87. f(x) = -,a =2 88. f(x) = - 1+x ,0 =3 1+r 1-I 89. f(x) = -,a = 2 90. f(x) = -.0 =3 2+ 1 2 91. f(x) = 1+7210=2 92. f(I) = 2+72:0=1 2 93. f(x) = 1+ 7310 =2 94. f(x) = 2+ 23:0=1 95. f(x) = 7210 =2 1+ 12 96. f(I) = 2+72:0=1 10 20 97. f(x) = 1+ VE ,a=1 98. f(x) = 2+ V a=1 99. f(x) = \\1+ vz,a =1 100. f(x) = \\2+ Vz,a =1 101. f(x) = (10Inx)/x, a = 2 102. f(x) = In(r + 2), a =1 103. f(x) =re , a=1 104. f(x) =r'e , a=1 105. f(z) = 4-x2 if x -1 1 0=-1 n 106. f(x) = -x3 if x 0 ,=0