math8 - Practice problems for midterm 3 1. Find the...

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Unformatted text preview: Practice problems for midterm 3 1. Find the dimension of a rectangle with parimeter 100 m whose area is as large as possible. 2. Find a positive number such that the sum of this number and its reciprocal is as small as possible. 3. If 1200 cm 2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box. 4. Find the point on the line 6 x + y = 9 that is closest to the point (-3,1). 5. Find the area of the largest rectangle that can be inscribed in the ellipse x 2 /a 2 + y 2 /b 2 = 1. 6. Find the most general antiderivative of the function (a) f ( x ) = 1 2 + 3 4 x 2- 4 5 x 3 (b) f ( x ) = ( x + 1)(2 x- 1) (c) f ( x ) = 5 x 1 / 4- 7 x 3 / 4 (d) f ( x ) = 6 x- 6 x (e) f ( u ) = u 4 3 u u 2 (f) f ( x ) = 3 e x + 7 sec 2 x (g) f ( t ) = sin t + 2 sinh t 7. Find f (a) f ( x ) = 6 x + 12 x 2 (b) f ( x ) = 1- 6 x and f (0) = 8 8. Express the area under f as a limit....
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math8 - Practice problems for midterm 3 1. Find the...

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