WEB–APPENDIX K
TAYLOR SERIES APPROXIMATION
Taylor series approximations are used in both mathematical economics and the economic theory of finance. They are widely used in numerical methods for evaluating a function around a particular value of its argument and consequently are discussed in every basic calculus book. We are here interested in the main result of Taylor's theorem for evaluating the function y = f(x) around a point a in its domain in terms of its derivatives.
Taylor's theorem (one-dimensional case):
where ! ≡ factorial. If we define x = a + h, or h = x − a, we may write the above more compactly as
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