The Lagrange Remainder Theorem provides a way to express the error or remainder of approximating a function by its Taylor series. It states that the remainder of the Taylor series for a function at a point can be represented as a specific term involving the (n+1)th derivative of the function, evaluated at some point between the center of expansion and the point of interest. This theorem is crucial in understanding how accurately a Taylor series can approximate a function, which is particularly useful in applications involving Taylor series.
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