These Ten-Year-Series (TYS) worked solutions with video explanations for 2011 A Level H2 Mathematics Paper 1 Question 4 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2011 A Level H2 Math Paper 1 Question 4
(i)
Use the first three non-zero terms of the Maclaurin series for $\cos x$ to find the Maclaurin series for $\text{g}\left( x \right)$, where $\text{g}\left( x \right)={{\cos }^{6}}x$, up to and including the term in ${{x}^{4}}$.
[3]
(i) Use the first three non-zero terms of the Maclaurin series for $\cos x$ to find the Maclaurin series for $\text{g}\left( x \right)$, where $\text{g}\left( x \right)={{\cos }^{6}}x$, up to and including the term in ${{x}^{4}}$.
[3]
(ii)
(ii)(a) Use your answer to part (i) to give an approximation for $\int_{0}^{a}{\text{g}\left( x \right)}\text{ d}x$ in terms of $a$, and evaluate this approximation in the case where $a=\frac{1}{4}\pi $.
[3]
(a) Use your answer to part (i) to give an approximation for $\int_{0}^{a}{\text{g}\left( x \right)}\text{ d}x$ in terms of $a$, and evaluate this approximation in the case where $a=\frac{1}{4}\pi $.
[3]
(b) Use your calculator to find an accurate value for $\int_{0}^{\frac{1}{4}\pi }{\text{g}\left( x \right)}\text{ d}x$. Why is the approximation in part (ii)(a) not very good?
[2]
(b) Use your calculator to find an accurate value for $\int_{0}^{\frac{1}{4}\pi }{\text{g}\left( x \right)}\text{ d}x$. Why is the approximation in part (ii)(a) not very good?
[2]
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