Use an appropriate Taylor polynomial about 0 and the Lagrange Remainder Formula to approximate sin(6/7) with an error less than 0.0001. What is the smallest value of n for which the approximation above is guaranteed to have an error less than 0.0001? (Be careful. Think about the actual terms used in the series as well as the remainder.) Let f(x) = Sigma^infinity_n=1 and g(x) = x^3 f (x^2/16). Let sigma^infinity_n=0 be the Taylor series of g about 0. The radius of convergence for the Taylor series for f is and the radius of convergence for the Taylor series for g is. Find each of the following coefficients for the Taylor series for g.
