Lagrange's Remainder Theorem provides a way to estimate the error when approximating a function using its Taylor series. It specifically states that the remainder of the Taylor series after n terms can be expressed as the value of the (n+1)-th derivative of the function at some point between the center of expansion and the point of approximation, multiplied by a power of the distance from that point. This theorem is essential for understanding error analysis and limitations in numerical approximations.
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