Monday, July 20, 2009

calculus - taylor and maclaurin series


This sketch shows the polynomial which represents the partial sum of the infinite series for a function. The sketch allows quick and continuous movement between each of the first ten polynomials centered at a (Taylor) or 0 (Maclaurin). The function can be changed, but Sketchpad calculates ten derivatives for each new function, which may be time consuming for some functions. By adding one term at a time, the user can watch as the approximating polynomial clings to curve of the original function and increases in its ability to describe the shape.

Keywords: calculus, Taylor, Maclaurin, series, infinite series, partial sum, polynomial, approximation, degree, derivative, power series

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