Taylor expansion commonly used in postgraduate entrance examination is as follows: If a function is derivative of order n, then this function is expanded into order n by Taylor formula, that is, f (x) =f(x0)/0! +f(x0)(x-0)/ 1！ +f"(x0)(x-x0)2/2！ +...+f(n)(x0)(x-x0)2/n！ +Rn(x). The remainder of Taylor formula can be used to estimate the approximate error.

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Taylor's formula is to approximate a function f(x) with an N-order polynomial about (x-x0) with an N-order derivative at x=x0. The expansion of Taylor formula refers to Taylor series of finite terms of function. In practical application, Taylor formula needs to be truncated and only takes a limited term, and the remainder of Taylor formula can be used to estimate the approximate error value. Taylor expansion commonly used in postgraduate entrance examination is that if the function f (x) has n-order derivative in a certain interval la, b], it contains X0.

And there is a derivative of order (n+ 1) in the open interval (a, b), then the expansion of the corresponding Taylor formula is f (x) =f(x0)/0 for any point x in the closed interval a, bl! +f(x0)(x-x0)/ 1！ +f"(x0)(x-x0)2/2！ +...+f(n)(x0)(x-x0)2/n！ +Rn(x). In addition, the commonly used Taylor formula expansions for postgraduate entrance examination are sinx=x- 1/6x3+o(x3), arcsinx=X+ 1/6x3+o(x3), and Tanx = x+1/3x3+.

Taylor formula is a formula that uses the information of a function at a certain point to describe its nearby value. If the function meets certain conditions, Taylor formula can use the derivative values of each order of the function at a certain point as coefficients to construct a polynomial to approximate the function.

Taylor formula is named after British mathematician Brook Taylor, who first described it in a letter 17 12. Taylor formula is one of the commonly used approximate methods to study the properties of complex functions, and it is also an important application content of function differential calculus.