Unformatted text preview: 5 ). Taylor Polynomials The higher derivatives of a function of one variable can be used to construct a polynomial that has highorder contact with the function at a point, and hence is a better local approximation to the function. An analogous construction is possible for functions of several variables, however more work is needed to combine the various partial derivatives of a given order into the appropriate polynomial. A polynomial in several variables consists of monomial terms, each involving powers of the di±erent variables; the degree of the term is the exponent sum : the sum of the exponents of all the variables appearing in that term. 15 Thus, each of the monomial terms 3 x 2 yz 3 , 2 xyz 4 and 5 x 6 has 15 The variables that don’t appear have exponent zero...
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 Fall '08
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 Calculus, Derivative, Limits, lim, △x

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