Let f(x) = X" and g(x) = x3 f (x2/25). Let anxn be the Taylor series of g about 0. The radius of convergence for the Taylor series for f is 1 and the radius of convergence n=1 the Taylor series for g is 5 Find each of the following coefficients the Taylor series for g. a4 = az = a2n+3 = ak = if k + 2n+3

(-1)^n! 1) Suppose we know that f(n) (4) = and the Taylor series of f 3n (n+1) centered at 4 converges to f(x) for all x in the interval of convergence. Show that the fifth-degree Taylor polynomial approximates f(5) with error less than 0.0002.