# 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.
1
2012-10-24T09:19:14-0400

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