be organizee slove the problem step by step show work and please try to in a paper

Problem Set 3 Due date: 09/20/2023 (11:59 PM) Problem 5. Problem 1. (a) What is the distance d between the points (3, 8) and (15, 13)? Fill in the tables and draw the graphs of the following functions: (b) (-4, 4) and (-3, 8); (a) X 0 1 2 3 4 g (x) = -2x +5 (a) (2, 3) and (5, 5); (b X 2 -1 0 1 2 3 4 Problem 6. h(x) = x2 -2x -3 Examine where the following functions are increasing/decreasing (use the result in (6.3.6)): x -2 -1 0 1 2 (c F(x) = 3* (a) f(x) = x2 - 6x + 5 (b) f(x) = -2(x+2) (x-6) Problem 2. Problem 7. (a) Consider the demand and supply curves D = 240 - AP and S = 2P - 30. Find the equilibrium price p*, and the corresponding quantity Q*. Determine the following limits: (a) lim (x2 -e* + 3) 2x + 3 (b) Suppose a tax of $4.50 per unit is imposed on the producer. How will this influence the equilibrium (b) lim - X-+0 * +2 x+ 2 price? Compute the total revenue obtained by the producer before the tax is imposed (R*) and after (R). (d) lim vx + 16 (e) lim - 1 - 3x x-+0 * +3 2-x Problem 3. Problem 8. Find formulas for the inverses of the following functions: (a) f(x) = 5-x3 (b) g(x) = In(1 + er) Find y' when 6 (a) y = - (b) y = 5x6/5 (c) y= = Problem 4. x2x-1/3 Problem 9. If f(x) =x2 -2x and g(x) = 1-x2, compute A firm produces f(L) = VL + L units of a commodity when L units of labour are employed. The price a) f(x) + g(x) obtained per unit is p and price per unit of labour is w. b) - f (x ) + 38 (x ) (a) What is the profit function (L)? c) f(2) + 2g(2) (b) Find the value of L for which m'(L) = 0. d) fig(x)) e) g(f(0))