The so-called MacLaurin series expansion for sin x is given by: 3 5 7 3! 5! 7! 1) Prove that this expansion is actually a special case of the Taylor series studied in class. Hint: write down the 5th order Taylor series for sin x (use equation (1) in my notes) and make a wise choice for the value of a. sin x 2) Use the MacLaurin series for sin x to prove that the limit of _ is 1 when 3) Write a MATLAB script named HW2-q3 to plot sin x for- (using x increments of 0.1 for x); on the same plot, include the MacLaurin expansions for sinx using 1, 2, 3 and 4 terms over the same range. Use different line colors and include a legend to differentiate your plots 4) Write a second Matlab script named HW2_q4 to compute sin(t) using its MacLaurin expansion with up to 10 terms, and generate a plot that displays the remainder Rn as a function of the number of terms. What conclusions can you draw from your results to questions 3) and 4)