MAC3472StudyGuideTest2

MAC3472StudyGuideTest2 - Study Sheet for Test 2 Honors...

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Study Sheet for Test 2 Honors Calculus Keesling Test on 10/9/07 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. Suppose that x 0 is an estimate of a solution to the equation f ( x ) = 0 . Newton used the tangent line to the graph of f at the point x 0 to find another approximation that is generally better. Derive the formula for the point x 1 that is where this tangent line crosses the x –axis. 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.

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MAC3472StudyGuideTest2 - Study Sheet for Test 2 Honors...

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