These Ten-Year-Series (TYS) worked solutions with video explanations for 2008 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
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Let $\text{f}\left( x \right)={{\text{e}}^{x}}\sin x$.
(i)
Sketch the graph of $y=\text{f}\left( x \right)$ for $-3\le x\le 3$.
(i) Sketch the graph of $y=\text{f}\left( x \right)$ for $-3\le x\le 3$.
(ii)
Using MF26, find the series expansion of $\text{f}\left( x \right)$ in ascending powers of $x$, up to and including the term in ${{x}^{3}}$.
(ii) Using MF26, find the series expansion of $\text{f}\left( x \right)$ in ascending powers of $x$, up to and including the term in ${{x}^{3}}$.
Denote the answer to part (ii) by $\text{g}\left( x \right)$.
(iii)
On the same diagram as in part (i), sketch the graph of $y=\text{g}\left( x \right)$. Label the two graphs clearly.
(iii) On the same diagram as in part (i), sketch the graph of $y=\text{g}\left( x \right)$. Label the two graphs clearly.
(iv)
Find, for $-3\le x\le 3$, the set of values of $x$ for which the value of $\text{g}\left( x \right)$ is within $\pm 0.5$ of the value of $\text{f}\left( x \right)$.
(iv) Find, for $-3\le x\le 3$, the set of values of $x$ for which the value of $\text{g}\left( x \right)$ is within $\pm 0.5$ of the value of $\text{f}\left( x \right)$.
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