Taylor's Theorem provides a way to approximate a function using polynomials, specifically by expressing a function as an infinite sum of its derivatives evaluated at a specific point. This theorem is foundational for understanding how functions behave locally and serves as the basis for deriving Taylor and Maclaurin series, which are used to represent functions in calculus. By utilizing the Mean Value Theorem, Taylor's Theorem demonstrates the relationship between derivatives and the behavior of functions near a point, leading to applications in various fields through the use of Taylor Series.
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