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Please show all work and box the final
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All problems are worth 25 points for a total of 250 points. Please show all of your work. tan x lim #1.) Find the limit: x-0 4x y = (x2 +1}\x? +2 = #2.) Find y' for dy #3.) Find dx by implicit differentiation: Vx+ y + Vxy = 6 = #4.) A man starts walking north at 4ft/s from a point P. Five minutes later a woman starts walking south at 5ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking? #5.) Find the point on the line 2x+3y + 5 = 0 that is closest to the point (-1,-2). scos Ve VE -dx #6.) Evaluate √x #7.) Evaluate S\x? +1 (**)dx #8.) Find the area of the region bounded by y = : 4x2 and y = x² + 3 = #9.) Find the volume of revolution if the area bounded by y = x² +1 and Y = 3 – x2 is revolved around the x-axis. #10.) Use the method of cylindrical shells to find the volume obtained by rotating the region bounded = x? :9 by about the x-axis. y and Y =