If a surveyor measures differences in elevation when making plans for a highway across a desert, corrections must be made for the curvature of the Earth. Compare the corrections given by the formulas in parts (a) and (b) for a highway that is 100 km long. (Take the radius of the Earth to be 6370 km.) From part (a): showing that the correction is C  =  R sec(L/R) − R From part (b): using Taylor polynomial to show C  ≈  L^2/2R + 5L^4/24R^3

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