2026 RVHS P1 Q1
2026 RVHS P1 Q1
Junior College 2
6 marks
It is given that \(y=\tan^{-1}(px)\), where \(p\) is a constant and \(-\frac\pi2<\tan^{-1}(px)<\frac\pi2\).
- Show that \((1+p^2x^2)\frac{\mathrm{d}y}{\mathrm{d}x}=p\).[2]
- By further differentiation of the result in part (a), find the first two non-zero terms in the Maclaurin series for \(y\).[4]
Solution:
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Answer:(a) Shown (b) \(px-\frac{p^3x^3}{3}\) for \(p\ne0\)
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