The series sin x = x 11! converges to sinx for all x. a) Find the first six terms of a series for cos x. For what values of x should the series converge? b) By replacing x by 2x in the series for sin x, find a series that converges to sin 2x for all x. c) Using the result in part (a) and series multiplication, calculate the first six terms of a series for 2 sin x COS x. Compare your answer with the answer in part (b).

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