Existing Fence Cows Goats Sheep бх 4x 2x A farmer wishes to build rectangular enclosures against an existing fence to keep the farm animals separated. All dimensions are in metres and the farmer has 1000 metres of fencing. All lengths shown on the diagram need to be constructed except, of course, the existing fence. (i) Show clearly why 12x + 4y = 1000 1 If the total area of the three enclosures is A m² ; Prove A = 3000x – 36x² (ii) 1

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A: To find the following limits. (c) limx→0+ lnxln1+x (d) limx→∞ xπ2-arctanx

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.