If f(x,y) = 3y' - 2xy - 13y + 4x- + 5x+ 6 then fy equals O 1 Does Not Exist 18y O - 2 0 8 O -2y + 8x + 5 O gy2 - 2x - 13Suppose the price of land in a city is given by the function 1 2 2 P(X,y) = 425 10(x 3) 15(y 1) where P(X,y) is the price of land at the point (X,y) in dollars per square metre and X and y are measured in kilometres. At what point within the city is the price of land highest? 7', (0,0) 5) None of the other answers 1%) 11,1) 2 2 Revenue. Suppose the graph of the revenue R00 and cost C(x) are shown below where R(x) = x22.5x+2 and C(x) = x2 + 2 The prot, or the area enclosed between the two curves is Note: Round to 4 digits after the decimai point, if rounding is required -6.9375 10.6667 10.6667 0 0.651 .~- 6.9375 none of the other answers ,. -0.651 Fundamental Theorem of Calculus. The Fundamental Theorem of Calculus says: Integration and Differentiation complement each other in Calculus Integration and Differentiation are inverse processes up to additive constants The integral of the derivative of a real function is the function itself The derivative of the integral of a real function is the function itself " All of the statements are true Below is the graph of a piecewise function f(x). y 4 3 2 1 X 6 -5-4 -3-2 -1 1 2 3 4 5 6 -1 -2 - 3 y = f(x) (a) lim f(x)= X- -47 0 3 0 2 0 1 O DNE 0 -3 (b) Is f(x) differentiable at x = 4? o true o false (c) Find the domain of f(x). o [-6,6) o [-6,2) U (2,6) o [-6,-4) U (-4,6) o (-6,-4) U (-4,6) o [-6,6] o (-6,-4) U (-4,2) U (2, 6) o [-6,-4) U (-4,2) U (2,6) o (-6,2) U (2, 6) (d) Find the range of f(x). o (-3,2) U (2,4] o (-3,1) U (1,4] o (-3,4] o [-3,4] o (-3,3) o [-3,2) U (2,4] o [-3,3] o [-3,1) U (1,4 ]Determine whether the following statement is true or false. If f and g are both decreasing on (a, b), then f - g is decreasing on (a, b). True O FalseDomain. The domain of 40 X - 6 g ( x) = 21x2 - 189x + 420 can be written: O [-4,5) U (5,00) O (-00,5) U (5,-6) U (-6,00) [-00,-4) U (-4,00) (-00,6) U (6,-5) U (-5,00 ) None of the other answers O (-4,-5) U (-5,00) O [6,00) O [-4,-6) U (-6,00)Integration by Substitution. The rate of growth of Grass carp, one of the most common type of fish, was modelled by the equation 3x+6 x2+4x+2 f(t) = where t is measured in years and t) in kilograms per year. Consider the integral [2 3x+6 2dX O x +4x+2 After substitution into u, the new integral can be written b fidu a U (a) The value ofA is 3x+2 6 3 x+2 0 1.5 x 3x (b) The upper limit of integration b is Sales. Suppose a tricycle company projects sales to increase with the function f(x) = 3x- + 2x Using the definition of the derivative, f'(x) is equal to O lim 3h2+ 6hx + 2h h - 0 h None of the other answers 3h-+ 6hx + 2h O h Oh - 0 lim 3h2 + 6hx + 2h 3h2 + 3hx + 2h h 3h- + 6hx O h lim 3h-+ 3hx + 2h O h - 0 h lim 3h- + 6hx O h - 0 h3 _ 2 Limits. Evalute Iim w rounded to 4 decimal places. X'7 x2 9x+ 14 m1 Q Does Not Exist or 00 (\"I 0.0595 O 16.8 If\") None of the other answers (*7. o O 0.5 f\") 2