1. Using the Maclaurin series for f(x) = sin x, derive the Maclaurin series for g(x) Hint: It is not necessary to do any differentiation to do this problem. = x sin 2x. 2. By multiplying the appropriate Taylor series about c = 0, compute the first four terms of the Taylor series about c = 0 for f(x) = ex cos x. Hint: It is not necessary to do any differentiation to do this problem. 3. Compute the Taylor series of f(x) = √√x about c = 1. v Hint: The first two terms don't fit the pattern of the remaining terms, so you will need to write those two terms out before writing the rest of the series compactly as an infinite series. This one is a bit messier than most of the examples we've seen up to this point. 4. Write the value of fe² dx as an infinite series.