Science:Math Exam Resources/Courses/MATH101 C/April 2025/Question 05/Hint 1

Remember that if the Taylor series of a function $f(x)$ is given by $f(x)=\sum _{n=0}^{\mathrm{\infty }}{a}_n{x}^n$, the Taylor series of $f(x^m)$ and $x^{m}f(x)$ are given by $$\begin{array}{r}f(x^m)=\sum _{n=0}^{\mathrm{\infty }}{a}_n{x}^{nm}\text{and}{x}^{m}f(x)=\sum _{n=0}^{\mathrm{\infty }}{a}_n{x}^{n+m}.\end{array}$$