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(Sec. 9.6 ~ 9.8, 7.1~7.6) (Take home, May 16, 2022) 1. Use the Ratio Test to determine the convergence or divergence of the series. Zn=0 5n 2. Use the Root Test to determine the convergence or 3n divergence of the series. Zn=1 - 3n 2n+1, 3. Find the Maclaurin polynomial of degree 6 for f (x) = cos x .4. Find the radius of convergence of the power series Joo (3x)n Ln=0 n 5. The region bounded by the graphs of y = x'- 4x2+ 3x, y=0. Then find the area of the region from x=0 to x=3. 4 2 X -2 6. Find the volume of the solid generated when the region bound by y = Vx , y = 0, and x = 9 is revolved about the line x = 9.7. Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region of y = x, x = 1, y = 0 about the x-axis 8. Find the distance between the points (1, 2), (3, 6) using arc length integration, then verify with the Distance Formula