Question 1: [15 Marks] Critically discuss the Maclaurin's Series in representing mathematical functions as power series. Question 2: [25 Marks] A milk retailer wishes to design a milk carton with a square cross-section, as illustrated in Figure 1. containing two pints of milk (2 pints = 1.136 litres). The carton is made from a rectangular sheet of waxed cardboard. It folds it into a square tube, seals down the edge, and then folds and seals the top and bottom. To make the resulting carton airtight and robust for handling, an overlap of at least 5mm is needed. The procedure is illustrated in Figure 2. As the milk retailer will be using many such cartons, there is a requirement to use the design that is least expensive to produce. In particular, the retailer desires a design that minimizes the amount of waxed cardboard used. Determine the dimensions of the container as per retailer requirements. 5 mm overlap INI h h Fresh Milk 2 pints (1.136 liters) IN b 5 mm overlap 50 mm is thermal conductivity, h is heat transfer coefficient, and t is the inner thickness of the insulation tube. Show that the critical thickness is at: k hi t=