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**Unformatted text preview: **power series on its interval of convergence. Find a power series representation f ( x ). Let F ( x ) denote an anti-derivative of f , ﬁnd the power series representation for F and f Compute their radius and interval of convergence. 4. Let f ( x ) = sin(2 x ). Find the 8th degree Taylor polynomial for f centered at the origin. Estimate the error in approximating sin(1) using this Taylor polynomial. How large a degree is required in order to approximate sin(1) to within 4 decimal places. 1...

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