... the root. The graph below shows what I am actually doing. Every time I am using the middle value x of the interval, and find the corresponding y value, then I will get a new but a smaller range. The more steps I do, then closer to the exact root value I will get. from the results I get from the spreadsheet, the root lies between the interval (1.88500977, 1.88525391), error bound = 0.00012207 root = 1.88513184 ± 0.00012207 Occasions in which the interval bisection causes problems: Although in the example above the interval bisection method worked fairly well, there are some cases in which it does not work. 1) One of the condition is that when there are several roots in one interval chosen. For example, y = (x-0.1)(x-0.2)(x-0.25)+1 From this graph we choose the interval as (0,1), then calculate f(0.5), then f(0.25), f(0.125), finally arriving at the root x=0.1. Indeed, there is one root ...

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