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This document discusses Taylor series approximations and estimating remainders. It explores approximating sin(x) using Taylor polynomials centered at x=0, and finds the interval (-r, r) where the approximation error is less than 10-8 when using a 7th degree Taylor polynomial. By estimating the remainder term, it determines that (-0.1, 0.1) is the interval where the approximation will be valid to within 10-8. The document also examines approximating another function using Taylor series and noting the regions

Author

abbey

Language

EN