Question: The power series for f(x) = is defined as 1+ x + x2 + x3 +... = > x, and the power series for sinx

 The power series for f(x) = is defined as 1+ x

The power series for f(x) = is defined as 1+ x + x2 + x3 +... = > x, and the power series for sinx is defined as x [ (-10 x20-1 1 - X n=0 31 51 7! (2n-1)! Part A: Find the general term of the power series for g(x) = 4 and evaluate the infinite sum when x = 1. Justify your solution. (15 points) X2 12 Part B: Find an upper bound for the error of the approximation sin(0.3) ko,3_(0:3) Round your final answer to five decimal places. (15 points) 3 Part C: Find a power series for h(x) = In(1 - x) centered at x = 0 and show the work that leads to your conclusion. (10 points)

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