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section 4.1 1. Find the indefinite integral.
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2. Find the indefinite integral.
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3. Find the indefinite integral.
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4. Find the indefinite integral.
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5. Find the indefinite integral.
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6. Find the indefinite integral.
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7. Find the indefinite integral.
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8. Find the indefinite integral.
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9. Find the indefinite integral.
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10. Find the indefinite integral.
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11. a. Verify that b. Graph the five functions 1/3 x 3 – 2, 1/3 x 3 – 1, 1/3 x 3, 1/3 x 3 + 1, 1/3 x 3 + 2, on the window [-3, 3] and [-5, 5]. c. Find the derivatives at x = 2 of the five functions in part b. c. For x = 2, the slope of each curve is 4. Thus, the derivative of each curve is x 2.
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12.BUSINESS: Cost – A company’s marginal cost function is MC = 20 x 3/2 – 15 x 2/3 + 1, where x is the number of units, and fixed cost are $4000. Find the cost function.
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13. BUSINESS: Revenue – A company’s marginal revenue function is MR = 12 x 1/3 + 3 x ½, where x is the number of units. Find the revenue function.
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14.GENERAL : Learning – A person can memorize words at a rate of 3/ t words per minute. a.Find a formula for the total number of words that can be memorized in t minutes. b.Use that formula to find the total number of words that can be memorized in 25 minutes. b. After 25 minutes, the total number of words memorized is N(25) = 6(25) 1/2 = 30 words
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15.ENVIRONMENTAL SCIENCE: Pollution – A chemical plant is adding pollution to a lake at the rate of 40 t 3 tons per year, where t is the number of years that the plant has been in operation. a. Find a formula for the total amount of pollution that will enter the lake in the first t years of the plant’s operation. b. Use the formula that you just found to find out how much pollution will enter the lake in the first 4 years of the plant’s operation. c. If all life in the lake will cease when 400 tons of pollution have entered the lake, will the lake live beyond 4 years? b. P(4) = 16(4) 5/ 2 = 512 tons Thus, 512 tons of pollution will enter the lake in the first four years of the plant’s operation. c. No, since 512 > 400.
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