2021 YIJC P1 Q8
It is given that $y=\sin \left( \ln \left( 1+\text{e}x \right) \right)$.
(i)
Show that ${{\left( 1+\text{e}x \right)}^{2}}\frac{{{\text{d}}^{2}}y}{\text{d}{{x}^{2}}}+\text{e}\left( 1+\text{e}x \right)\frac{\text{d}y}{\text{d}x}=-{{\text{e}}^{2}}y$.
[2]
(ii)
By further differentiation of the result in (i), find the Maclaurin series for $y$, up to and including the term in ${{x}^{3}}$.
[4]
(iii)
By using appropriate standard series expansions from the List of Formulae (MF26), verify the correctness of the Maclaurin series for $y=\sin \left( \ln \left( 1+\text{e}x \right) \right)$ found in part (ii).
[2]
Suggested Handwritten and Video Solutions
Share with your friends!
WhatsApp
Telegram
Facebook