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Explain the term linear approximation.
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Answer / kitty
In mathematics, the process of finding a straight line that
closely fits a curve (function) at some location. Expressed
as the linear equation y = ax + b, the values of a and b
are chosen so that the line meets the curve at the chosen
location, or value of x, and the slope of the line equals
the rate of change of the curve (derivative of the
function) at that location. For most curves, linear
approximations are good only very close to the chosen x.
Yet much of the theory of calculus, including the
fundamental theorem of calculus and the mean-value theorem
for derivatives, is based on such approximations.
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