section 4.1. 1. Find the indefinite integral. 2. Find the indefinite integral. 3. Find the indefinite integral. 4. Find the indefinite integral. 5. Find the indefinite integral. 6. Find the indefinite integral. 7. Find the indefinite integral. 8. Find the indefinite integral.
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1. Find the indefinite integral.
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 x2 .
MR = 12 x 1/3 + 3 x ½ , where x is the number of units. Find the revenue function.
GENERAL : Learning – A person can memorize words at a rate of 3/t words per minute.
b. After 25 minutes, the total number of words
memorized is N(25) = 6(25) 1/2 = 30 words
ENVIRONMENTAL SCIENCE: Pollution – A chemical plant is adding pollution to a lake at the rate of 40t 3 tons per year, where t is the number of years that the plant has been in operation.
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
c. No, since 512 > 400.