 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2/4/solution

ln (1 + x^{2}) = x^{2} - x^{4} /2 + O (x^{6})

(1 + x^{2})^{- 1} = 1 - x^{2} + O (x^{4})

. The first two nonzero terms are

\frac{ln ( 1 + x ^{2} )}{1 + x ^{2}} = x^{2} - \frac{3}{2} x^{4} + O (x^{6}) .

 New to topics? Read the docs here!