FE 0708 sem2 (Solutions and Remarks)

# FE 0708 sem2 (Solutions and Remarks) - Qn 18. (Final...

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Qn 18. (Final Examination AY0708 Sem 2) Do you have the solution to the fnal exam paper? Ans. I don’t have the solutions to the fle, so I wrote a sketch here. I did not fnish the questions, because I want to tell you the answer is not important, the most important thing is understand the solution steps and the tricks. Question 1 [10 marks] (a) Let x =2+ t 2 +cos t and y =3+2 t 4 +sin t . Find the value of dy dx at the point when t = π 2 . Solution. Remark. Final examination will test all the chapters and all the tutorials. For Chapter 1-4, the questions will be much more diﬃcult than the mid-term. 22

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(b) A (circular) cylindrical container with no top cover is to be constructed to hold a fxed volume V cm 3 oF liquid. The cost oF the material used For thebaseis8cents/cm 2 , and the cost oF the material used For the curved surFace is 3 cents/cm 2 . ±ind the radius r cm (in terms oF V ) oF the least expensive container. Solution. Remark. If you use surface integral to get the value of lateral area, that will be a waste of time. Some mathematical formulas that you have learnt in primary / secondary school will be short-cuts of the questions. 23
Question 2 [10 marks] (a) The fnite region R in the frst quadrant is bounded by the curve y = e x , and the lines y = e 2 and x = 1. Find the volume o± the solid generated when R is revolved about the line x =1 . ( Give the exact volume in terms of π and e . ) Solution. 24

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(b) Find the sum of the following in±nite series inside the interval of conver- gence 1 1 3 ( x 8) + 1 9 ( x 8) 2 + ··· + x 8 3 ± n + ··· Solution.
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## This note was uploaded on 05/05/2009 for the course MA MA1505 taught by Professor Ma1505 during the Spring '09 term at National University of Juridical Sciences.

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FE 0708 sem2 (Solutions and Remarks) - Qn 18. (Final...

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