 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/19/b/solution

e^{- x} = 1 - x + x^{2} /2 + O (x^{3})

(1 + x)^{- 1/2} = 1 - x /2 + 3 x^{2} /8 + O (x^{3})

. The constant, linear and quadratic coefficients are therefore

e^{- x} (1 + x)^{- 1/2} = 1 - \frac{3}{2} x + \frac{11}{8} x^{2} + O (x^{3}) .

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