Arrington AMath 0120 Examination #3SampleName (Print) PeopleSoft # . Signature Score . TA (Circle one) Instructions:1. Clearly print your name and PeopleSoft number and sign your name in the space above. 2. There are 8 problems, each worth the specified number of points, for a total of 100 points. There is also an extra-credit problem worth up to 5 points. 3. Please work each problem in the space provided. Extra space is available on the back of each exam sheet. Clearly identify the problem for which the space is required when using the backs of sheets. 4. Show all calculations and display answers clearly. Unjustified answers will receive no credit. 5. Write neatly and legibly. Cross out any work that you do not wish to be considered for grading. 6No calculators, headphones, tables, books, notes, or computers may be used. All derivatives are to be found by learned methods of calculus.Arrington A1. Let x1)x(f . (a) (5 pts.) Approximate the area under the curve y = f(x) from a = 1 to b = 13 using a Riemann sum with 3 left rectangles. (Write the sum; you need not evaluate it.) (b) (5 pts.) Find the exact area under the curve y = f(x), 1 ≤ x ≤ 13, using the Fundamental Theorem of Calculus.2. (15 pts.) Find the following integrals: (a)dx)e1x(43 (b) 131)x( dx (c) x12xdxArrington A3. (16 pts.) Use substitution to find the following integrals: (a) 232)x3x)(1x(dx (b) 8132x3xedx 4. (6 pts.) For the demand function D(p) = p3175 (a) Find the elasticity of demand, E(p). (b) Is demand elastic, inelastic, or unitary at p = 50?Arrington A 5. (7 pts.) A company’s marginal cost function is MC(x) = 4x - 6e-0.1x where x is the number of units and fixed costs are $65. Find the cost function. 6. (16 pts.) Set up, but do not evaluate, integrals for the area (a) Between the curves y = x and y = x2 on [-1,1]. (b) Bounded by the curves y = 4x – x2 and y = x2.Arrington A7. (6 pts.) Given a demand function of d(x) = 300 – 0.4x and a supply function of s(x) = 0.2x. (a) Find the market demand (the positive value of x at which the demand function intersects the supply function). (b) Set up, but do not evaluate a definite integral for the producers’ surplus at the market demand.8. (24 pts.) Use integration by parts to find: (a) )xlnx(2dx (b)x2xedx (c) 5xxdxArrington A(5 pts) Extra-Credit : You may earn an extra 5 points by evaluating 20dx)4x( without using the Fundamental Theorem of
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