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StudyGuideTest2(2008)

# StudyGuideTest2(2008) - Study Sheet for Test 2 Honors...

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Study Sheet for Test 2 Honors Calculus Keesling Test on 10/22/08 1. State the Mean Value Theorem. 2. Suppose that ! f ( x ) < 1 for all x in x 0 ! " , x 0 + " [ ] and that f ( x 0 ) = x 0 . Let x 1 ! x 0 " # , x 0 + # [ ] with x 1 ! x 0 . Show that f ( x 1 ) ! x 0 < x 1 ! x 0 . This says that f ( x 1 ) is closer to x 0 than x 1 . 3. Let f ( x ) = 0 be an equation to be solved numerically. Let g ( x ) = x ! f ( x ) " f ( x ) . Show that the set of values where f ( x ) = 0 is precisely the set of values where g ( x ) = x . 4. Solve the following equations using Newton’s Method. (a) x 3 ! 5 = 0 (b) x 9 + sin x = 10 (c) tan x = 2 5. Find the right circular cylinder of greatest volume that can be inscribed in a sphere of radius R . Find the right circular cylinder having greatest surface area that can be inscribed in a sphere of radius 10. 6. Find the right circular cone of greatest volume that can be inscribed in a sphere of radius R . Find the one with greatest surface area for R = 10 . 7. A wire of length 100 cm is cut into two pieces. One piece is bent into a circle, the other into a square. Where should the cut be made to maximize the sum of the areas of the square and the circle? To minimize that sum? 8. Determine the numbers x and y such that x ! y is maximum subject to x + y = 10 and x ! 0

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StudyGuideTest2(2008) - Study Sheet for Test 2 Honors...

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