These Ten-Year-Series (TYS) worked solutions with video explanations for 2019 A Level H2 Mathematics Paper 2 Question 4 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2019 A Level H2 Math Paper 2 Question 4
(i)
Given that $\text{f}\left( x \right)=\sec 2x$, find $\text{f}’\left( x \right)$ and $\text{f}”\left( x \right)$. Hence, or otherwise, find the Maclaurin series for $\text{f}\left( x \right)$, up to and including the term in ${{x}^{2}}$.
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(i) Given that $\text{f}\left( x \right)=\sec 2x$, find $\text{f}’\left( x \right)$ and $\text{f}”\left( x \right)$. Hence, or otherwise, find the Maclaurin series for $\text{f}\left( x \right)$, up to and including the term in ${{x}^{2}}$.
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(ii)
Use your series from part (i) to estimate $\int_{0}^{0.02}{\sec 2x\text{d}x}$, correct to $5$ decimal places.
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(ii) Use your series from part (i) to estimate $\int_{0}^{0.02}{\sec 2x\text{d}x}$, correct to $5$ decimal places.
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(iii)
Use your calculator to find $\int_{0}^{0.02}{\sec 2x\text{d}x}$, correct to $5$ decimal places.
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(iii) Use your calculator to find $\int_{0}^{0.02}{\sec 2x\text{d}x}$, correct to $5$ decimal places.
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(iv)
Comparing your answers to parts (ii) and (iii), and with reference to the value of $x$, comment on the accuracy of your approximations.
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(iv) Comparing your answers to parts (ii) and (iii), and with reference to the value of $x$, comment on the accuracy of your approximations.
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(v)
Explain why a Maclaurin series for $\text{g}\left( x \right)=\operatorname{cosec}2x$ cannot be found.
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(v) Explain why a Maclaurin series for $\text{g}\left( x \right)=\operatorname{cosec}2x$ cannot be found.
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