Academy of Chinese Culture and Health Sciences Calculus Quiz Questions

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Academy of Chinese Culture and Health Sciences

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Calculus problems

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CHAP. 12] INTEGRAL CALCULUS 333 INTEGRATION BY SUBSTITUTION 12.47. Use integration by substitution to determine the indefinite integral for each of the following functions: (a) / 252x² (7x3 - 12)2 dx (b) / 90x® (3x4 + 1994 dx (c) S 672x (8x2 – 9) dx 120x3 dx (5x4 - 18) -576x2 (e) / dx 30x+ (8x + 13) - dx 6x5-21 18.23 dx 9x4-5 (h) / 99x2 22x3 + 19dx (i) | 96x?q4xdx (j) / 120re-ar dx INTEGRATION BY PARTS 12.48. Use integration by parts to determine each of the following indefinite integrals: (a) / 20x(x + 9)4 dx (h) 42x(x – 3) dx 36.x (c) S dx -182 (x + 8)S (d) S (x-7)3 dx 6x (e)s d. VX+13 (f) / 45xVx+21dx (g) 7xet-3 dx (h) | 32.x2e4x dx 12.49. A firm's marginal cost function is MC = x2 - 11x + 385. Its fixed costs are $450. Find the total cost TC function. 12.50. Find a firm's total cost of producing 3 extra units as a firm moves from a production level of 4 units to 7 units, given MC = 3x2 - 4x + 525. 12.51. Find a fimm's total revenue TR function, given the marginal revenue function MR = -0.24x2 - 1.5x + 660. 12.52 Estimate the additional total revenue received from increasing sales from 10 to 12 units, given MR = 104 - 6x. 12.53. A car worth $6000 depreciates over the years at the rate V'(0) = 250(1-6) for 0
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