In this question you may use expansions from the List of Formulae (MF26). Find the first four non-ze

Question

In this question you may use expansions from the List of Formulae (MF26). Find the first four non-zero terms of the Maclaurin series of ${{\mathrm{e}}^{-x}}\left( 1+\cos 3x \right)$, in ascending powers of $x$. [4] It is given that the first three terms of this series are equal to the first three terms in the series expansion, in ascending powers of $x$, of $\frac{1}{a+bx}+c{{x}^{2}}$. Find the values of $a$, $b$ and $c$. [4]

Accepted Answer

(a) $2-2x-\frac72x^2+\frac{25}{6}x^3+\cdots$. (b) $a=\frac12, b=\frac12, c=-\frac{11}{2}$.

2023 RI Promo Q5

2023 RI Promo Q5

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