Subject Code : MAST10006
Assignment Task

Question 1

In this question you must state if you use any standard limits, limit laws, continuity, l’Hˆopital’s rule or the sandwich theorem.

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Question 2

In this question you must state if you use any standard limits, limit laws, continuity, l’Hˆopital’s rule, the sandwich theorem or convergence tests for series

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Question 3

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Question 6 (13 marks) A lake of volume 6 GL (gigalitres) contains fresh water. A river flows into the lake at a rate of 24 GL per year, mixes uniformly with the lake water, and flows out the other side of the lake at the same rate of 24 GL per year. An industrial accident upstream of the lake releases a pollutant into the river. Let x(t) be the amount (in tonnes) of pollutant in the lake at time t years after the accident.

(a) Suppose that the river water flowing into the lake contains pollutant at a constant concentration of 0.5 tonnes per GL. Assume that the lake initially contains no pollutant.

(i) Show that x(t) is described by the ordinary di↵erential equation (ODE)

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  • Uploaded By : Alon 
  • Posted on : October 17th, 2018
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