(a) The distance x of a runner from a fixed point is measured (in metres) at intervals of half a second. The data obtained are: t t x X 0.0 0.5 1.0 1.5 2.0 0.00 3.65 6.80 9.90 12.15 Use central differences to approximate the runners velocity at times t = 1.0 s and t = 1.75 s. (b) Use the midpoint rule with 4 intervals to approximate, correct to 3 decimal places, the area bounded by the curve y = ex², the x-axis, and the ordinates at x = 0 and x = 1.

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