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1. [5 points] Find a rectangle with the greath area. among all the rectangles with the fixed perimeter p. Express the maximum area. of the rectangle in terms of p. 2. [5 points} Sketch the graph of a function that satises Q of the following Conditions. Explain! - an) = u, and PH) = f'(1}= I19} = n :- zling\": at] = I] and lc) = oo o f'te} 4: i] on [oo. 2}, {LE}, and {91 oo} . me} e e on (11} and {as} o f\"[e]l :- i] on (oo,]l and (121m) :- fe} 4:: {I on {lL} and {6,12} 3. {1|} points} Show that the sum of the :r and yintereepts of an}; tangent line to the curve +=disequaltoe 4. (5 points) A faucet is filling a hemispherical basin of diameter Bi] cm with water at a rate of 2 Litfmin. Find the rate at which the water is rising in the basin 1when it is half full. Hint: The volume of the portion of a sphere with radius r from the bottom to a height it is given by V = '(i*ft2 it\"). 5. (15 points) Determine the following limits. Show work! (b) lim cotr - COST (c) lim tan r * (7/ 2)