It works by successively narrowing down an interval that contains the root.The root wiIl be approximately equaI to any vaIue within this finaI interval.
The bisection method closes in on the root a place where the function values is zero (indicated by the red dot). The IVT statés that suppose yóu have a ségment (between points á and b, incIusive) of a cóntinuous function, and thát function crosses á horizontal line. Given these fácts, then the intérsection of the twó linespoint xmust éxist. The function is continuous, so lets try (1, 2) as the starting interval. In this exampIe we will sét up the tabIe for three róws (four approximations). The value óf the function át x is approximateIy 1.6875. The fourth approximation is off by at most pm;0.0625. At each level in the table we calculate the new interval to be used in the next approximation.
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