It is given that $\mathrm{f}(x) = \frac{1}{\sqrt{1-4x^2}}$ where \(-\frac{1}{2}

Question

It is given that $\mathrm{f}(x) = \frac{1}{\sqrt{1-4x^2}}$ where $-\frac{1}{2} < x < \frac{1}{2}$. Using standard series from the List of Formulae (MF27), find the Maclaurin's expansion of $\mathrm{f}(x)$, up to and including the term in $x^6$.[2] Hence find the first four non-zero terms of the Maclaurin series for $\sin^{-1} 2x$.[4]

Accepted Answer

(a) $1+2x^2+6x^4+20x^6+O(x^8)$. (b) $2x+\frac43x^3+\frac{12}{5}x^5+\frac{40}{7}x^7+O(x^9)$.

2025 ACJC P2 Q2

2025 ACJC P2 Q2

Solution:

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