58 the sum of the perimeters of an equilateral

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58. The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions of the triangle and the square that produce a minimum total area. 59. Two posts, one 12 feet high and the other 28 feet high, stand 30 feet apart. They are to be secured by two wires, attached to a single stake, running from ground level to the top of each post. How far from the left post should the stake be placed to use the least wire? 60. A manufacturer makes a metal can in the shape of a cylinder that holds 3 1000cm of oil. What radius and height will minimize the amount of metal in the can? 61. A cylindrical metal container, open at the top, is to have a capacity of 3 24 in . The cost of material used for the bottom of the container is \$0.15 per sq. in., and the cost of the material used for the curved part is \$0.05 per sq. in. Find the dimensions that will minimize the cost of the material, and find the minimum cost. Use the figure to find the limit. 62. 3 lim x f x 63. lim x f x   64. 2 lim x f x 65. 0 lim x f x 66. lim x f x    67. 5 lim x f x  
__________________________________________________________________________________ Find the limit. 68. 2 3 6 3 lim x x x x   69. 2 0 5 25 lim x x x 70. 0 1 1 lim x x x 71. 2 6 6 3 18 lim x x x x   72. 3 2 8 2 lim x x x   73. 2 2 3 5 4 1 lim x x x x   _____________________________________________________________________________________ Find the slope of the line tangent to the curve at the point P by using the formula: Slope of tangent line lim x c f x f c x c . (You must know this formula.) 74. 2 5 4, (2, 2) f x x x P 75. 6, (3,3) f x x P 76. 3 2 2 1, ( 2,1) f x x x P 77. 2 2 7 3, ( , ( )) f x x x P c f c 78. Find an equation of a line that is tangent to the curve 3 f x x and is parallel to the line 12 10 0 .

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