? ?. (i) Discuss the continuity of the function f(x) = {x2 − 3x if x < 2 2x + 4 if x ≥ 2on the open interval 0 < x < 2 and on the closed interval 0 ≤ x ≤ 2. (ii) An efficiency study of the morning shift at a certain factory indicates that an average worker arriving on the job at 7:00 A.M.will have assembled f (x) = x3 + 6x2 + 15x units x hours later. Approximately how many units will the worker assemble between 8:00 and 8:15 A.M.? (iii) A manufacturer’s total cost is C(q) = 0.1q3 + 0.5q2 + 500q + 200 dollars when the level of production is q units. The current level of production is 4 units, and the manufacturer is planning to increase this to 4.1 units. Estimate how the total cost will change as a result.
? ?. (i) Discuss the continuity of the function f(x) = {x2 − 3x if x < 2 2x + 4 if x ≥ 2
on the open interval 0 < x < 2 and on the closed interval 0 ≤ x ≤ 2.
(ii) An efficiency study of the morning shift at a certain factory indicates that an average worker arriving on the job at 7:00 A.M.will have assembled f (x) = x3 + 6x2 + 15x units x hours later. Approximately how many units will the worker assemble between 8:00 and 8:15 A.M.?
(iii) A manufacturer’s total cost is C(q) = 0.1q3 + 0.5q2 + 500q + 200 dollars when the level of production is q units. The current level of production is 4 units, and the manufacturer is planning to increase this to 4.1 units. Estimate how the total cost will change as a result.
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