In this video I go over a brief introduction to Linear Approximation and explain why it is a very important tool and sometimes necessary in approximating the values of any function as opposed to directly calculating those functions which can be complicated and sometimes impossible.
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Linear Approximation - Introduction
Thus we can approximate f(x) as a linear function (i.e. a line) near x = a.
The idea is that it might be easy to calculate a value f(a) of a function, but difficult (or even impossible) to compute nearby values of f.
Thus we settle for the easily computable values of the linear function L(x)
This is called the Linear Approximation or Tangent Line Approximation of f at a.