# Answer to Question #17175 in C# for yo_jack

Question #17175
Use all programming techniques that you have learnt so far, approximate the root of f(x) = x3 - 3 with the bisection method starting with the interval [1, 2] and use &epsilon;step = 0.1 and &epsilon;abs = 0.1. Write a flowchart for your design. Hints: Initial Requirement: We have an initial bound [a, b] on the root, that is, f(a) and (b) have opposite signs. Iteration Process: Given the interval [a, b], define c = (a + b)/2. Then &bull;if f(c) = 0 (unlikely in practice), then halt, as we have found a root,. &bull;if f(c) and f(a) have opposite signs, then a root must lie on [a, c], so assign b = c,. &bull;else f(c) and f(b) must have opposite signs, and thus a root must lie on [c, b], so assign a = c.. Halting Conditions: There are three conditions which may cause the iteration process to halt: 1.As indicated, if f(c) = 0.. 2.We halt if both of the following conditions are met: ◦The width of the interval (after the assignment) is sufficiently small, that is b - a &lt; &epsilon;step, and. ◦The function evaluated at one of the end point |f(a)| or |f(b)| &lt; &epsilon;abs.. . If we halt due to Condition 1, we state that c is our approximation to the root. If we halt according to Condition 2, we choose either a or b, depending on whether |f(a)| &lt; |f(b)| or |f(a)| &gt; |f(b)|, respectively.
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2012-10-24T09:19:14-0400

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