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Maclaurin Series – Small Angle Approximation Q1 In the triangle $ABC$, angle $BAC=frac{pi }{3}$ radians, angle $ABC=left( frac{pi }{3}+x right)$ radians and angle $ACB=left( frac{pi }{3}-x right)$ radians, where $x$
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
These Ten-Year-Series (TYS) worked solutions with video explanations for 2004 A Level H2 Mathematics Paper 1 Question 1 are suggested by Mr Gan. For any comments or suggestions please contact
2022 SAJC P2 Q3 In this question you may use expansions from the List of Formulae (MF26). (i) Find the Maclaurin expansion of $ln left( 1+cos 3x right)$ in ascending
These Ten-Year-Series (TYS) worked solutions with video explanations for 2021 A Level H2 Mathematics Paper 1 Question 7 are suggested by Mr Gan. For any comments or suggestions please contact
These Ten-Year-Series (TYS) worked solutions with video explanations for 2020 A Level H2 Mathematics Paper 1 Question 3 are suggested by Mr Gan. For any comments or suggestions please contact
2020 VJC Promo Q1 It is given that $frac{text{d}y}{text{d}x}+xy={{text{e}}^{-x}}$ and $y=1$ when $x=0$. (i) Find the Maclaurin series for $y$, up to and including the term in ${{x}^{3}}$. [5] (ii)
2021 RI Promo Q5 (i) Using standard series from the List of Formulae (MF26), expand $frac{cos 3x}{4-x}$ as far as the term in ${{x}^{3}}$. Give the coefficients as exact fractions
2021 NYJC Promo Q7 It is given that $y=sqrt{1+ln left( 1+sin 2x right)}$. (i) Show that $yfrac{text{d}y}{text{d}x}=frac{cos 2x}{1+sin 2x}$. [1] (ii) Show that $yfrac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}+{{left( frac{text{d}y}{text{d}x} right)}^{2}}=frac{k}{left( 1+sin 2x right)}$, where
2020 TMJC Promo Q6 Do not use a calculator for this question (a) Give that $y={{text{e}}^{frac{2}{x+1}}}$, where $xne -1$, show that ${{(x+1)}^{2}}frac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}+2(x+2)frac{text{d}y}{text{d}x}=0$. By further differentiation of this result, or otherwise,