Consider non-dimensional differential equation for the height at the highest point is given by \begin{equation} h(\mu)= \frac{1}{\mu}- \frac{1}{\mu^2} \log_e(1+\mu) \end{equation} $0<\mu\ll 1.$ Deduce an estimate to $O(\mu)$ for $h(\mu)$ and compare with $t_h(\mu)=1-\frac{\mu}{2}+\cdots$
=> I really don't how to start this question. please help me.
If you know that $\log_e(1+\mu) = \mu - \dfrac{\mu^2}{2} + \dfrac{\mu^3}{3} - \dfrac{\mu^4}{4}+\cdots$ and plug that in, you get $\dfrac12- \dfrac\mu3+\dfrac{\mu^2}{4}+\cdots.$