Problem. 10 : Find the total differential of the function f(x, y) = 32 + 4 xy + 2x ? df = ( da + ( dy Problem. 11 : Find the total differential of the function f(x, y) = (342+62)3 ? df = ( da + ( dy Problem. 12 : Find the total differential of the function f(x, y, z) = 4 xy5 22 df = da + dy + dz Problem. 13 : Use differentials to estimate the change in f when the point (r, y) changes from (-2, 5 ) to (-1.96, 5.03 ). (Round your answer to three decimal places.) f(x, y) = -6xy2 - y3 + 2x2 ? Af~ Problem. 14 : Use differentials to estimate the change in f when the point (x, y) changes from (1, 1) to (1.01, 0.95 ). (Round your answer to three decimal places.) f(x, y) = vie" ? Af~ Problem. 15 : Gator FanStuff manufacures and sells r tailgate canopies and y coolers per week. The total weekly profit (in dollars) realized from these sales is given by the function P(x, y) = -0.20x2 - 0.25 y' - 0.10 xy + 70 x + 60 y-3900. Currently, the weekly output is 186 canopies and 115 coolers. Use differentials to estimate the change in weekly profit dP if management decides to increase the number of canopies to 191 and decrease the number of coolers to 107. (Round your answer to the nearest dollar.) dP =Problem. 16 : Gator Golf Cartz has = determined that it takes r units of labor and y units of capital to produce f(r, y) units of its product, where f(x, y) = 70 23/5 y2/5 . Find the approximate change in output df if the amount of labor is decreased from 60 to 55 units and the amount of capital is increased from 210 to 211 units. (Round your answers to two decimal places.) df ~ Problem. 17 : Evaluate the double integral of the function f(x, y) over the given region R. f(x, y) = 3r+7y; R is the rectangle defined by 4 $ r $ 7, 4 S y $ 7 Problem. 18 : Evaluate the double integral of the function f(x, y) over the given region R. f(x, y) = 12 xy' +6 y R is the rectangle defined by 1 x $ 6, 1 y $ 6 Problem. 19 : Evaluate the double integral of the function f(x, y) over the given region R. Round your answer to three decimal places.) f(x, y) = / R is the rectangle defined by 1 S a $ 2, 1 S y s 2 Problem. 20 : Evaluate the double integral of the function f(x, y) over the given region R. f(x, y) = x+4y R is bounded by r = 0, r = 3, y = 0, y = 3 x Problem. 21 : Evaluate the double integral of the function f(x, y) over the given region R. f(x, y) =3r+4y; R is bounded by x = 0, x = vy, y = 25Problem. 22 : Use a double integral to find the volume of the solid shown in the figure. 2 = 6 - y 4 3 cubic units Problem. 23 : Use a double integral to find the volume of the solid shown in the figure. 2. 2:5 y = 4 - x cubic units