Part 1
1. Find the centroid of the system consisting of a mass of 1 at (9, -2), a mass of 6 at (3, 0), a mass of 4 at (9, -7), and a mass of 2 at (-3, -2). You may enter your answer either as a decimal or a fraction. If you use decimal form, it must be accurate to within 0.001.
2. Find the centroid of the system consisting of a mass of 7 at (5, 5), a mass of 8 at (6, -1), a mass of 5 at (8, -2), and a mass of 5 at (7, 6). You may enter your answer either as a decimal or a fraction. If you use decimal form, it must be accurate to within 0.001.
3. Find the centroid of the region bounded by 3x - 2y = -16, 9x + 4y = -28, and x = 0. You should enter the coordinates of your answer either as decimals or fractions. Your answer must be accurate to within 0.001.
4. Find the centroid of the region bounded by 3x - 10y = -56, x - 10y = 28, x = -2, and x = 8. You should enter the coordinates of your answer either as decimals or fractions. Your answer must be accurate to within 0.001.
Part 2
Find the indicated Taylor and Maclaurin polynomials. You may enter the coefficients as integers, fractions, or decimals. If you enter the values as decimals, you will need to be accurate to 4 significant figures (the test is that your value differs from the true answer by .0005*abs(true value) or less). All problems are worth 6 points.
1. Find the second Taylor polynomial for f(x) = (6x + 10) / (x2 + x - 1), expanded about c = 1.
2. Find the fifth Maclaurin polynomial for f(x) = x3 cos (Sx).
3. Find the fifth Maclaurin polynomial for f(x) = x3 e-4x.