Given that $y={{\sin }^{-1}}(2x)$, show that \(\left( 1-4{{x}^{2}} \right){{\left( \frac{\mat

Question

Given that $y={{\sin }^{-1}}(2x)$, show that $\left( 1-4{{x}^{2}} \right){{\left( \frac{\mathrm{d}y}{\mathrm{d}x} \right)}^{2}}=4$[1] By further differentiation of this result, find the Maclaurin’s series of $y$ up to and including the term in ${{x}^{3}}$.[4]

Accepted Answer

$\displaystyle \sin^{-1}(2x)=2x+\frac43x^3+O(x^5)$

2013 AJC P1 Q4

2013 AJC P1 Q4

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