find these limits

Finding a Limit of a Trigonometric Function In Exercises 63-74, find the limit of the trigonometric function. sin x 3(1 - cos x) 63. lim 64. lim x 0 5x x 0 (sin x) (1 - cos x) cos tan 65. lim 66. lim x2 sin2 x tan x 67. lim 68. lim x 0 X X - cos h)2 69. lim 70. lim Nsec E h 0 h 6 - 6 cos x 71. lim 72. lim COS X - sin x - 1 x 0 3 x 0 2x sin 3t 73. lim 0 2t 74. lim sin 2x Hint: Find lim 2 sin 2x 3x x o sin 3x x 0 2x \\3 sin 3x) Graphical, Numerical, and Analytic Analysis In Exercises 75-82, use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. 75. lim Vx+ 2 - V2 76. lim 4 - Vx X X x 16 x - 16 - 32 77. lim [1/(2 + x)] - (1/2) 78. lim X X x 2 x-2 sin 3t cos x - 1 79. lim 80. lim x 0 2x2 sin x2 81. lim 82. lim sin x x 0 x 0 3x Finding a Limit In Exercises 83-90, find lim f (x + Xx) - f(x) Xk 83. f(x) = 3x - 2 84. f(x) = -6x + 3 85. f(x) = x2 - 4x 86. f(x) = 3x2 + 1 87. f(x) = 2 /x 88. f(x) = Vx - 5 89. f(x) = - 1 90. f(x) = x + 3