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Taylor series are widely used in various fields of science and engineering to approximate complex functions with polynomial expressions, making calculations simpler and more efficient. For example, they are essential in numerical methods for solving differential equations, optimizing algorithms in computer science, and modeling physical systems in physics and engineering. Additionally, Taylor series enable the analysis of functions near specific points, which is valuable in fields like economics for forecasting and in machine learning for optimization techniques. Overall, their ability to provide accurate approximations facilitates problem-solving across numerous applications.

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