MATH119 Study Guide - Absolute Convergence, Polynomial, Iterated Integral
7 Nov 2013
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Some methods (i. e. unintegratable ones) must be approximated, since we can not nd exact solutions. There are two such methods for approximation: analytic and numerical. For analytic approximation we make a simpli cation using the theory of calculus to recognize reasonable approximations, ie for any small x. sin x2 = x2. We refer to the de nition of a de nite integral, and calculate the area of n rectangles of width x n, and height determined by our function. Obviously, both of these methods can be useful. When using high-powered technology, the numerical approach can reach near-perfection, but analytical methods can still be useful to nd approximations without assigning random variables or to determine whether a numerical analysis is giving a realistic result. Linear approximation is also known as tangent line apprximation or linearization. The de nition of a derivative is f(cid:48)(a) = lim x a f (x) f (a) x a.
