It is given that ${{ an }^{-1}}y=a{{ an }^{-1}}x+b$, for constants $a$ and $b$. Show that $\left(

Question

It is given that ${{	an }^{-1}}y=a{{	an }^{-1}}x+b$, for constants $a$ and $b$. Show that $\left( 1+{{x}^{2}} ight)\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}=2\left( ay-x ight)\frac{\mathrm{d}y}{\mathrm{d}x}$. [2] 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]

Accepted Answer

$a=2$, $b= rac\pi4$, $c=4$

2022 NJC J2 CT P1 Q3

2022 NJC J2 CT P1 Q3

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