1. (15 points) Find the volume of the solid obtained by rotating the region bounded by y = x and y=x, with x 0 about the x-axis using the washer method. 2. (15 points) Find the volume of the solid obtained by rotating the region bounded by y = x3 and y=4x, with x 0 about the y-axis using the shell method. 3. (15 points) Solve the initial value problem y' = xycosx/(1+ y), y(0) = 1. 4. (10 points) Test for convergence. State which test your work is based on. (4 + n)/(n+3). 5. (15 points) Determine if the series converges or diverges. Show all your work and state convergence tests used. n/(2n-1). 6. (15 points) Determine if the following series converges or diverges. If it converges, find its sum. Show all your work and state a convergence test used. (3+4")/(5"). 7. (15 points) Determine if the series converges or diverges. Show all your work and state a convergence test used. 1/(nlnn). 2