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All the integrals below are understood in the sense of the Lebesgue.
(1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]. Then
(2) Assume that f is integrable over [0; 1]. Show that
is di erentiable a.e on (0; 1).
(3) Assume that f is continuous on [0; 1]. Suppose that
Average cost function : Now let's turn our attention to the average cost function. If C ( x ) is the cost function for some of the item then the average cost function is,
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Evaluate the given definite integral. Solution Let's begin looking at the first way of dealing along with the evaluation step. We'll have to be c
As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and holds 9 cubic
Given the following decision tree, perform the tasks listed below 1. Simulate the route through the test market and produce results for twenty simulations, calculating the
Reason for why limits not existing : In the previous section we saw two limits that did not. We saw that did not exist since the function did not settle down to a sing
Assume that between workers exposed to asbestos in a shipyard in 1980, 33 died over a 10 year period from COPD, whereas only 24 such deaths would be expected based on statewide mor
If cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?. Ans: Cos? + Sin? = √2 Cos? ⇒ ( Cos? + Sin?) 2 = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒
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#question Show that the enveloping cylinder of the conicoid ax 2 + by 2 + cz 2 = 1 with generators perpendicular to the z-axis meets the plane z = 0 in parabolas
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