(i) A business manager determines that t months after production begins on a new product, the number of units produced will be P thousand,where P(t) =6?^2 + 5? /(? + 1)^2. What happens to production in the long run ? (ii) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture.Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0),but for x > 0,it is found that y =0.5(x^2 + 3x) /x^3 + x^2 + 4x.Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?

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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.