A Primer of Calculus

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2/=(z-fl)2 (x— 3)S.
[min., x= — 1; max., x=2; min., a;=3].
82. w=x^ -{-y'', -where lx-\-my-\-n=o.
[_w =n^ / (Z^ -f-™^ )) ^ minimum] .
83. Find the largest rectanglar area that can be en- closed by a boundary of 200 feet. [2500 sq. feet.] 84. Find the largest rectangle that can be cut out of a circular sheet 6 feet in diarneter. [18 sq. feet.] 85. Find the altitude of the maximum rectangle that can be cut from an isoscles triangle, one side being part of the base. \_\ altitude triangle.] 86. Fin
...d the altitude of the maximum right cone that can be inscribed in a sphere of radius a.
[Let a+a:= altitude, 2/= radius of base =J(a^ — x^); ' a; ==^ a for required maximum.] 87. Find the basin of largest volume, round or square, that can be made with a given number of square feet of tin. [Width = double the height].
88. A Norman window consists of a rectangle sur- mounted by a semicircle. Given the perimeter of th§ 60 A PRIMER OF CALCULUS frame, what dimensions give the window that will admit most light.


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