The value of x3 is then chosen as either the midpoint of x0 and x2 or as the midpoint of x2 and x1, depending on whether x0 and x2 bracket the root, or x2 and \...The value of x3 is then chosen as either the midpoint of x0 and x2 or as the midpoint of x2 and x1, depending on whether x0 and x2 bracket the root, or x2 and x1 bracket the root. The algorithm proceeds in this fashion and is typically stopped when the increment to the left side of the bracket (above, given by (x1−x0)/2) is smaller than some required precision.
As we have studied limits, we have gained the intuition that limits measure 'where a function is heading.' We have seen, though, that this is not necessarily a good indicator of what the function actu...As we have studied limits, we have gained the intuition that limits measure 'where a function is heading.' We have seen, though, that this is not necessarily a good indicator of what the function actually is. This can be problematic; functions can tend to one value, but attain another. This section focuses on functions that do not exhibit such behavior.
