2022 NJC J2 CT P1 Q3
Timothy Gan
2022 NJC J2 CT P1 Q3
It is given that ${{\tan }^{-1}}y=a{{\tan }^{-1}}x+b$, for constants $a$ and $b$.
(i)
Show that $\left( 1+{{x}^{2}} \right)\frac{{{\text{d}}^{2}}y}{\text{d}{{x}^{2}}}=2\left( ay-x \right)\frac{\text{d}y}{\text{d}x}$.
[2]
(ii)
Suppose that the Maclaurin series for $y$ is $1+cx+8{{x}^{2}}+20{{x}^{3}}+…$. Find the exact values of $a$,$b$ and $c$.
[5]
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