Quest Assignment 2-solutions

# Quest Assignment 2-solutions - saliyev(is4663 Quest...

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saliyev (is4663) – Quest Assignment 2 – rodin – (54520) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Oil is ±owing From a well in a continuous stream at a rate oF f ( t )= 14000 ( t +5) 2 barrels per month. ²ind the total oil produced by the well during its liFetime operation. 1. #barre ls =3200 2. ls =3000 3. ls =2800 correct 4. ls =2400 5. ls =2600 Explanation: The liFetime production oF oil is given by the improper integral I = ± 0 f ( t ) dt = ± 0 14000 ( t 2 dt. As a limit I =l im s →∞ ± s 0 14000 ( t 2 dt oF proper integrals, thereFore, I s ² - 14000 ( t +5 ³ s 0 =2800 . Consequently, ls = 2800 . 002 10.0 points ²ind the area oF the region R defned by R = ´ ( x, y ): x ≥- 4 , 0 y e - x/ 7 µ . 1. Area( R )=7 e - 4 / 7 2. Area( R e 4 / 7 3. Area( R e 4 / 7 correct 4. Area( R e - 4 / 7 5. Area( R Explanation: The region R is the area below the graph oF y = e - x/ 7 on the infnite interval [ - 4 , ), and so looks like the shaded region in x y - 4 extended to + in the x -direction. Thus the area oF R is the limit lim t ± t - 4 e - x/ 7 dx . Now ± t - 4 e - x/ 7 dx = - 7 ² e - x/ 7 ³ t - 4 = - 7 e - t/ 7 +7 e 4 / 7 . Consequently, Area( R e 4 / 7 since lim x e - x =0 . 003 10.0 points

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saliyev (is4663) – Quest Assignment 2 – rodin – (54520) 2 Which (if any) of the following integrals is convergent? 1. ± - 5 6 x 2 dx 2. ± 5 3 x xdx 3. ± 5 0 4 x dx correct 4. none of them 5. ± 5 0 8 x x dx 6. ± 0 - 5 6 x 2 dx Explanation: Each of the improper integrals I = ± 5 0 1 x p dx, I = ± 0 - 5 1 x p dx is convergent if and only if p< 1, while each of I = ± 5 1 x p dx, I = ± - 5 1 x p dx is convergent if and only if p> 1. Of the given integrals, therefore, only I = ± 5 0 4 x dx is convergent.
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Quest Assignment 2-solutions - saliyev(is4663 Quest...

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