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Find the volume of the solid generated by revolving the region enclosed by the graph of x2 + y2 = a2 and the coordinate axes

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Find the volume of the solid generated by revolving the region enclosed by the graph of x\"2 + y\"2 = a\"2 and the coordinate axes about the x-axns. Use shells or washers as appropriate. When a particle is at the point x on the x-axis, it is acted upon by a force of sin 1tx Newtons. Find the work done by the force in moving the particle from x=1 to x=2 (x is measured in meters). go 2112 +n+1 Determine whether the series, 211:0 m converges or diverges. If it converges, find its limit. 3 1/1: Determine whether the series, 233:0 converges or diverges. If it n2 converges, find its limit. sinn Determine whether the series, Zn=1 n n+1 converges or diverges. If it converges, find its limit.Test the series for convergence or divergence. ( .)" Z 3.; Include answers to the following questions along with your work to determine convergence: a. What was your first impression as to which test/method to use on the series and why? b. If you had to start over and try a different test, explain which you chose next and why. What did you learn from your first attempt that you incorporated into your next attempt? c. Do you think it would be possible to determine convergence for this series in another way? Why or why not? Find the radius of convergence and the interval of convergence of Find a power series representation for the function and determine the radius of convergence. =W -2x Find the Taylor series for f (x) = e centered at a = 1. State the radius of convergence

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