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solutiontoexam3_pdf - rabbani(tar547 Review Exam 3...

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Unformatted text preview: rabbani (tar547) Review Exam 3 Fouli (58395) 1 This print-out should have 33 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A rectangle is inscribed between the y-axis and the parabola y 2 = 75 x as shown in Determine the maximum possible area, A max , of the rectangle. 1. A max = 504 sq. units 2. A max = 500 sq. units correct 3. A max = 501 sq. units 4. A max = 502 sq. units 5. A max = 503 sq. units Explanation: Let ( x, y ) be the coordinates of the upper right corner of the rectangle. The area of the rectangle is then given by A ( y ) = 2 xy = 150 y 2 y 3 . Differentiating A ( y ) with respect to y we see that A ( y ) = 150 6 y 2 . The critical points of A are thus the solutions of 150 6 y 2 = 0 , i . e ., y = 5 , 5 ; the solution y = 5 can obviously be disre- garded for practical reasons. Substituting for y = 5 in A ( y ) we get A max = 500 sq. units . 002 10.0 points Circuit City has been selling 70 television sets a week at $400 each. A market survey indicates that for each $20 rebate offered to a buyer, the number of sets sold will increase by 5 per week. How large a rebate should Circuit City offer a buyer in order to maximize its revenue? 1. rebate = $60 correct 2. rebate = $70 3. rebate = $65 4. none of these 5. rebate = $75 6. rebate = $55 Explanation: Let $20 x be the rebate offered to a buyer. Then the price of a TV will be $(400 20 x ) and the number of sets sold at this price will be 70 + 5 x . The revenue with this rebate is thus R ( x ) = (400 20 x )(70 + 5 x ) = 100(20 x )(14 + x ) = 100(280 + 6 x x 2 ) . But then R ( x ) = 100(6 2 x ) , while R ( x ) = 100 2 < . rabbani (tar547) Review Exam 3 Fouli (58395) 2 Consequently, the Revenue is maximized at x = 3, in which case the rebate = $60 . 003 10.0 points Use Newtons method to estimate the solu- tion to e 2 x + x = 4 5 starting with the initial guess x = 0 and applying one iteration. 1. estimate = 1 5 correct 2. estimate = 3 10 3. estimate = 1 2 4. estimate = 1 10 5. estimate = 2 5 Explanation: If x n is one estimate of a solution to the equation f ( x ) = 0, then Newtons method says that x n +1 = x n f ( x n ) f ( x n ) will usually be a better estimate. But when f ( x ) = e 2 x + x 4 5 , then f ( x ) = 2 e 2 x + 1 , so Newtons method gives the iteration for- mula x n +1 = x n e 2 x n + x n 4 5 2 e 2 x n + 1 . Consequently, with an initial guess of x = 0, x 1 = 0 1 4 5 2 + 1 = 1 5 . 004 10.0 points Find the value of f (0) when f ( t ) = 2(3 t + 4) and f (1) = 1 , f (1) = 6 ....
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solutiontoexam3_pdf - rabbani(tar547 Review Exam 3...

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