It is given that $y=\sqrt{1+\ln(1+2x)}$. Show that \(y\left(\dfrac{ \mathrm{d}y}{ \mathr

Question

It is given that $y=\sqrt{1+\ln(1+2x)}$. Show that $y\left(\dfrac{ \mathrm{d}y}{ \mathrm{d}x}\right)=\dfrac{1}{1+2x}$. [1] By further differentiation, obtain the Maclaurin series of $y$, up to and including the term in $x^2$.[3] Hence, find the Maclaurin series of $\dfrac{1}{\left(1+\ln(1+2x)\right)^{\frac{3}{2}}},$ up to and including the term in $x^2$. [3]

Accepted Answer

$y=1+x-\dfrac32x^2+\cdots$; required series $=1-3x+\dfrac{21}{2}x^2+\cdots$

2025 RVHS Promo Q8

2025 RVHS Promo Q8

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