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Example 1
Given the data points ..., 3.2, 3.3, 3.4, 3.5, 3.6, ... which measure the rotation of a satellite dish at points in time, with angles 1.05837 1.15775 1.25554 1.35078 1.44252, approximate the rate of change of the angle at time 3.4 using both the 1st-order and 2nd-order backward divided-difference formulae.
(1.25554 − 1.15775)/0.1 = 0.9779 and (1.05837 − 4⋅1.15775 + 3⋅1.25554)/(2⋅0.1) = 0.970285.
Thus, 0.970285 is the more accurate answer. The data was taken from a curve which has an exact derivative of 0.96680 at 3.4.
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