Reference: Calculus and Its Applications, 12th, by Marvin L. Bittinger and David Ellenbogen Book

Elementary Applied Calculus

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\fUse geometry to evaluate the definite integral. 90 x dx x dx = (Simplify your answer.) 9Use geometry to evaluate the definite integral. 10 SX dx 0 10 -X dx = (Type an integer or a simplified fraction.)A company's total cost, in millions of dollars, is given by C(t) = 70 -40e " where t is the time in years since the start-up date. The graph of C(t) is shown to the right. Find each of the following 150- a) The marginal cost, C'(t) b) C'(0) c) C'(6) d) Find lim C(t) and lim C'(t). 75- 1-+00 1-+00 0 15 30 a) C'(t) =(Do not include the $ symbol in your answer.) b) C'(0) = $ million per year (Simplify your answer. Do not include the $ symbol in your answer.) c) C'(6) = $ per year (Simplify your answer. Round to the nearest thousand as needed. Do not include the $ symbol in your answer.) d) lim C(t) = $ million 1-+00 (Simplify your answer. Do not include the $ symbol in your answer.) lim C'(t) = $ per year 1-+00D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. Find (a) the equilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point. D(x) =3500 - 40x, S(x) = 800 + 5x (a) What are the coordinates of the equilibrium point? (Type an ordered pair.) (b) What is the consumer surplus at the equilibrium point? $(Round to the nearest cent as needed.) (c) What is the producer surplus at the equilibrium point? 5(Round to the nearest cent as needed.)List the points in the graph at which the function is not differentiable. Ay X XO X1 X2 X3 X4 X5 Select all that apply. B. X2 A. X4 OD. X1 OC. X5 F. XO DE. X3