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 us at support@timganmath.edu.sg.
2021 A Level H2 Math Paper 1 Question 7
It is given that $y={{\text{e}}^{{{\sin }^{-1}}x}}$, for $-1<x<1$.
(a)
Show that $\left( 1-{{x}^{2}} \right)\frac{{{\text{d}}^{2}}y}{\text{d}{{x}^{2}}}=x\frac{\text{d}y}{\text{d}x}+y$.
[4]
(a) Show that $\left( 1-{{x}^{2}} \right)\frac{{{\text{d}}^{2}}y}{\text{d}{{x}^{2}}}=x\frac{\text{d}y}{\text{d}x}+y$.
[4]
(b)
Find the first $4$ terms of the Maclaurin expansion of ${{\text{e}}^{{{\sin }^{-1}}x}}$.
[5]
(b) Find the first $4$ terms of the Maclaurin expansion of ${{\text{e}}^{{{\sin }^{-1}}x}}$.
[5]
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