Taylor's Polynomial

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   Purpose of the calculations carried out here is to estimate values of many times differentiable real function of real variable in vicinity of a point in which its value and values of several of its higher order derivatives are exactly known. Given coordinate of the point, value of the function in that point and values of its derivatives of order one to n, we construct a polynomial of degree n or less having in the given point the same value and the same values of its derivatives as the the function. The value of the function in any other point is then estimated as equal to the value of the polynomial in that point.
   First applet constructs the Taylor's polynomial. Type the coordinate of the point, the value of the function and values of its derivatives of increasing order in that point in the left input field , one number per line. The click submit. The right text field then contains the coefficients of the polynomial in column vector form, starting at the top with coefficient at zero power of independent variable and ending with the coefficient at power equal to the degree of the polynomial.
   Second applet calculates values of any polynomial and its first and second derivative in any point x. Type the coefficients of the polynomial in column vector form in left input field and click enter or click copy to transfer the polynomial found in the first applet to the second. Then type the desired value of the independent variable in the upper right input field and click calculate.

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