MDN: MAC2233, Practice Test 4 Name:______________________________MDN: MAC2233, Practice Test 4 Name:______________________________Chapters 5.1 – 5.5 Date: Show all possible work on this test paper.1. Evaluate ( )x x dx- +�58 4 7.2. Find the function whose tangent line has the slope x -39 4 for each value of x, and whose graph passes through (3, -2).3. Evaluate xe dxx-� �-� �� ��854. Evaluatex dxx x� �- +� �� ��3535 5775. Evaluate xdxx -�5634Page 1 of 46. Evaluate ( )xx e dx�987. Evaluate the indicated integral:x xdxx x x+ ++ + +�4 35 43 12 65 10 128. Evaluate xdx� �+� �� ��37389. Evaluate ( )x-+�5627 3 . Express your answer as a decimal. Approximate to one decimal. Page 2 of 410. Evaluate dxx x� �+ -� �� ��5528 95.11. Evaluate x dxx� �+� �+� ��73411512. Evaluate dxx+�34135 2 Approximate your answer to two decimal places.13. Determine the area of the region bounded by the curves y = 2 + 5x – 2/3x2 and y = x2 + 2. (Hint: Sketch the graph or solve the two equations simultaneously.)Page 3 of 414. Sketch the region R and then use calculus to find the area of R. R is the region between the curve y = x4 and the line y = 15x - 14 for x 0 .15. Find the Gini index for the given Lorentz curve: L(x) = 0.2x2 + .25x.16. Find the average value of xx-35 over the interval 1 ≤ x ≤ e317. At a factory a machine that is t years old is generating revenue at a rate ofR’(t) = 20,000 – 50t2 dollars a year and is generating costs at a rate of C’(t) = 5,000 + 10t2 dollars a year. [a] What is the useful life of the machine(round to nearest year), and [b] compute the net profit generated by themachine over its useful life.Page 4 of
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