Bisection Method for Approximating Zeros of a Function f

Chapter 5, Problem 115

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Bisection Method for Approximating Zeros of a Function f We begin with two consecutive integers, a and , such that and are of opposite sign. Evaluate f at the midpoint of a and .If , then is the zero of f, and we are finished. Otherwise, is of opposite sign to either or . Suppose that it is and that are of opposite sign. Now evaluate f at the midpoint of a and .Repeat this process until the desired degree of accuracy is obtained. Note that each iteration places the zero in an interval whose length is half that of the previous interval. Use the bisection method to approximate the zero of in the interval correct to three decimal places. [Hint: The process ends when both endpoints agree to the desired number of decimal places.]