 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1/15/a/solution

sinh t = t + t^{3} /3! + t^{5} /5! + O (t^{7})

, applied with

t = x^{2}

and then multiplied by

x

, gives

x sinh (x^{2}) = x^{3} + \frac{x ^{7}}{6} + \frac{x ^{11}}{120} + O (x^{15}) .

These are the first three nonzero terms. The remainder is written in Big O notation.

 New to topics? Read the docs here!