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Unformatted text preview: ⊂ [2 , 3]. Note that this was a pretty arbitrary choice, the main goal was to make it easy to check the conditions of the ﬁxed point theorem. 4. For part (b) try something similar to the previous problem. 5. Just use the formula for Newton’s method. Note that for f ( x ) =x 3cos x we have that f ( x ) =3 x 2 + sin x so that f (0) = 0 so it will not be possible to carry out the Newton iteration if 0 is chosen as the initial point because carrying out the ﬁrst step of the iteration requires dividing by f (0) = 0. Geometrically Newton’s method calculates the zero of the tangent line at the initial point. If f ( p ) = 0 then the tangent line at p is horizontal and does not have a zero. 1 6. See Burden and Faires for some pseudo  code for these methods. 2...
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 Spring '08
 hitrik
 Math, Calculus, Intermediate Value Theorem, Continuous function, Order theory, Fixed point

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