6, Find the two first-order partial derivatives as well as ALL second-order partial derivatives for each of the following functions: (a) z = xy2; (b) z = ylna 7, Suppose estimated production function for a certain fishery is F(S, E) = 2.26.$0.44 F0.48 where S denotes the stock of lobsters, E the harvesting effort, and F(S, E) the catch. (a) Find the first-order partial derivatives Fs and FE. (b) Show that SFs + EFE = kF for a suitable constant k. 8, Suppose that if a household consumes a units of one good and y units of a second good, its satisfaction is measured by the function s(x, y) = 2Inx + 4ly Now suppose that the household presently consumes 20 units of the first good and 30 units of the second good. What is the approximate increase in satisfaction from consuming one extra unit of: (a) the first good? (b) the second good? 9, (bonus points) Suppose limn +(n) = x. Show that lim (can) = cx for all c E R n -+0o