Taylor Series for cos(x)
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This applet demonstrates approximations of the cosine function using Taylor series. Key math concepts include calculus, polynomial functions, and sequences. It is constructed using GeoGebra's Sum command with objects like function f, variable n, graph g, and text2. Suitable for high school and above students learning calculus and function approximation.
GeoGebra Commands & Parameters
Sum(Sequence[(((-1)^(i) * x^((2 * i)))) / ((2 * i))!, i, 0, n, 1]) → g
AI Drawing Prompt Reference
Draw a graph showing the approximation of the cosine function using Taylor series, where the curve of the cosine function and the curve of its polynomial approximation gradually approach each other as the number of terms increases, accompanied by a text label indicating the current number of terms in the series, starting with simple low-order approximations and gradually increasing to show the convergence effect.
The prompt above was compiled from the original drawing commands and is for reference only.