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{til 9. 10. . [1U points] Compute lim :I:+tan:r 32}0 9 sin 1' . 1U oints Find the e uation of the tan ent line to the curve 43:2 + 5-1: + 2 2 = 79 at the P (1 g y 3; point {1, 5). (10 points) Use the definition of the derivative to compute the derivative of f (11.) = %. [Do not use derivative rules for this problem] (1U points] Let Ffr] = gfs). If 9(3) = 6, g'{:l:1)=4J f'{3] = 4, and f'j) = 7, nd F'fii). (10 points) A box with no top and a square base has a volume of 32 m\". If the box has the least possible surface area, nd its dimensions {nd side length of base square and find height of box). (10 points) 1Water is pouring into a swimming pool at a constant rate of 3 cubic feet per second. The pool is shaped like a cylinder with radius 6 feet and height 6 feet. Find the rate of change of the height of the water at the moment when the water is 4 feet high. . Let r) = 2:3 123: + 6. (a) Find the critical points of Hr). (b) Find everywhere H13) is increasing and everywhere x] is decreasing. (c) Find any local extrema {nd all local max and local min, if any) . Let y = {3-32 + 5..)2. Find dy when :1? = 2 and {3 = [1.3. (a) Find the tangent line to at) = V3: + 2 at :13 = 14. (b) Use the tangent line to approximate V131 by hand. 4 2 2 + 7 Compute / 3: d3