1. [4 marks] Suppose that a company has determined its marginal revenue to be R'(x) = 50 ( 2+ 2 dollars per unit. Determine the company's revenue when x = 1000 units are sold. You may assume that the company's revenue is $0 when no units are sold. [Hint: 2 = 1 + 1] I 2. [2 marks] Given that / f(x)dx = -2 and / f(x)dx - 5, use properties of definite integrals to evaluate / f(x)dx. 3. [11 marks] Suppose that f(x) = 100- - 23 . 1 1 12 + 72% 8C ~ to search PrtSc F8 F10 F12 F9 F11 F2 C F7 F3 X F4 F5 F6 & 5 6 7 8 O N 3 4 O P W E R T S D F G H K(b) In Maple, to approximate (and obtain a picture of) the area between f(x) and the x-axis over [0, 6] using right endpoints and n = 3 equal width subintervals enter: with(Student [Calculus1]): ApproximateInt(100-(x/3),x=0..6,partition=3,method=right,output=plot) Record the result in the appropriate cell of the table below:(or clearly labeled on your own paper). Complete the table for the varying values of n using the i) right endpoint, ii) left endpoint, and iii) midpoint of each subinterval. n 3 30 300 i) Area using Right Endpoints ii) Area using Left Endpoints iii) Area using Midpoints (c) Use Maple to find the exact value of f(x)dz. area:=Int(100-(x/3),x=0..6); value(area) (d) Recall that [ f()de = lim - a [f (at' i). .Verify the result in part (c) by evaluating this limit. Type here to search