1. What is the Maclaurin series for the function sin(x)? Please determine the minimum number of terms needed to compute sin(0.1) accurate to 12 decimal places (rounded), using a) Taylors theorem and b) alternating series theorem.

Show your work and justify your answers for the above problem. 2. Create two random matrices A and B each of size . Write a computer program in Java or Matlab to compute

a) D(i, j) = A(i, j) * B(i, j) for i = 1 n and j = 1 n, and

b) D(i, j) = (A(i,k) B(k,j)) =1 for i= 1 n and j = 1 n.

Use a timing function to report the execution time for the two computations using single and then double precisions. Report on the execution time of each run. Try n = 100 and 1000.

c) repeat the calculations in (a) and (b) above using Matlab.

1. What is the Maclaurin series for the function sin(x)? Please determine the minimum number of terms needed to compute sin(0.1) accurate to 12 decimal places (rounded), using a) Taylor's theorem and b) alternating series theorem. Show your work and justify your answers for the above problem. 2. Create two random matrices A and B each of size n x n. Write a computer program to compute a) D(i, j) = A(i, j) * B(i, j) for i=1 ... n and j=1 ... n, and b) Di, j) = XR-1(Ai, k) * B(k,j)) for i=1 ... n and j = 1 ... n. Use a timing function to report the execution time for the two computations using single and then double precisions. Report on the execution time of each run. Try n= 100 and 1000. c) repeat the calculations in (a) and (b) above using Matlab