Consider the function f(x) = sin(x) Part a. Compute the Maclaurin series of this function. Part b. Compute the Taylor series of f centered at x = /3. Part c. Plot partial sums of your Maclaurin and Taylor series approximation with varying number of terms in the approximations to obtain an idea of how the Maclaurin and Taylor series approximations begin to approximate the function as you increase the number of terms in the series. Part d. Use your results from part a to compute the Maclaurin series of cos(x). Hint: recall that cos(X) =[sin(x)]. Part e. Use your results from part d to compute the Maclaurin series of g(x) = x cos(x). Plot one or two partial sums to verify your Maclaurin series approximation of g.