MATHEMATICS -content– 1) Simplify: (5xy7)3(3x5y3)4 2) Find the equation for the line passing through the points (4,1) and (6, 19) in slope-intercept form 3) Assume that the value of a machine is a linear function of time. When new the machine is worth $50,000. Four years later the machine is worth 36,500. When will the machine be worth exactly $5000? 4) Solve the equation: 3x 3 + 5x 2 – 8x – 23 = 0. Compute the solutions with 2 decimal place accuracy. 5) Identify the critical values of the function 6) Find the domain and range of the function: f(x) = ? 3? x 7) Let f(x) = x2 + 4x + 5 and g(x) = 4x – 3. Compute a) (f (g(4)) b) (f (g (5)) c) (g (f (x)) 8) Let h(x) = (3x 2 + 7)4 – 2(3x 2 + 7)2 . Find two functions f and g such that f(g(x)) = h(x) 9) Compute the following limit: 4 lim x ? 64 16 3 2 ? ? x x 10) Compute the following limit: 4 lim x ? 2 16 2 ? ? x x Compute the derivatives of the following functions by any means (11 through 17) 11) f(x) = 5 x 12) g(x) = 6x 5 – 5x 4 + 7x 2 + 5x + 4 13) q(x) = (2x 3 – 5) 7 14) n(x) = 4 4 4 x x ? f(x) = x3 – 12x 2 + 5 15) q(x) = ( ) 3 3 x x ? x 16) r(x) = 1 2 x ? x 17) u(x) = x (3x + 4)5 18) Find the equation for the tangent line to the curve f(x) = 3x 3 – 2x 2 – 5 at x = 2 19) You are in a race. The distance you travel from the starting gate in t seconds is h(t) = t3 + 2t 2 + 3t feet. a) How far have you traveled 3 seconds after the start of the race? b) What is your velocity 3 seconds after the start of the race? c) What is your acceleration 3 seconds after the start of the race? 20) Find the absolute maximum and absolute minimum of the function f(x) = x3 – 3x 2 on the interval [-1,4] 21) The height of a ball ‘t’ seconds after you throw it is h(t) = 32t – 16t2 feet. What is the maximum height the ball will reach and when will it reach that maximum height? 22) You own a company that makes necklaces. There is no initial start-up costs, but it costs you $40 a piece to manufacture each necklace. If you manufacture x necklaces you can sell them at (160 – x) dollars a piece. How many necklaces should you make in order to maximize your profits and what is your maximum profit? 23) You are going to build a rectangular yard against the side of a barn (so you do not have to make the fourth side) using 1200 feet of fence. What should the dimensions of the yard be in order to maximize the area of the yard and what is the maximum area? 24) You can sell 6 cars if you charge $16,000 a car. For every $100 you reduce the price you can sell one additional car. How many cars would you sell and what price should you charge in order to maximize revenues, and what is your maximum revenue? 25) An apple grower finds that if she plants 20 trees per acre, each tree will produce 100 bushels of apples. For each additional tree she plants each tree will produce 2 less bushels. How many trees should she plant per acre in order to maximize her harvest? PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET A GOOD DISCOUNT

2016-09-21