Please help!! show all steps and be clear :)thanks 2 1. (12 pts) Evaluate the integral dx

Please help!! show all steps and be clear :)thanks

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2 1. (12 pts) Evaluate the integral dx ;x>1 x" [trig substitution] 3. (12pts) Use the integral test to determine whether the series IM8 n=1 -1 8 tan n 1+m converges or diverges. [Assume the 3 conditions for this test are satisfied, NO need to prove them] x x- sin x 6. (12 pts) Use power series to evaluate the limit. lim 2 0+x x [HINT: use the series expansion from the Cheat Sheet]. SHOW WORK 8. (14pts) a. Find the volume of the solid generated by rotating the region bounded 2 by the equations x ==, x=0, y=1, y=4, y about the y-axis. b. Sketch the region, the solid, and a typical disk or washer. 2 1. (12 pts) Evaluate the integral dx ;x>1 x" [trig substitution] 3. (12pts) Use the integral test to determine whether the series IM8 n=1 -1 8 tan n 1+m converges or diverges. [Assume the 3 conditions for this test are satisfied, NO need to prove them] x x- sin x 6. (12 pts) Use power series to evaluate the limit. lim 2 0+x x [HINT: use the series expansion from the Cheat Sheet]. SHOW WORK 8. (14pts) a. Find the volume of the solid generated by rotating the region bounded 2 by the equations x ==, x=0, y=1, y=4, y about the y-axis. b. Sketch the region, the solid, and a typical disk or washer.