The curve $C$ has equation $y=3-2\ln(1+x)$. Sketch the graph of $C$, stating clearly the exact

Question

The curve $C$ has equation $y=3-2\ln(1+x)$. Sketch the graph of $C$, stating clearly the exact coordinates of the axial intercepts and equations of the asymptotes (if any).[3] Find the exact equation of the tangent to $C$ at the point where $x=\frac{1}{2}$, giving your answer in the form $y=ax+b$, where $a$ and $b$ are constants to be determined.[4] On the graph in part (i), sketch the graph of the tangent to $C$ at $x=\frac{1}{2}$, stating clearly the coordinates of the axial intercepts.[2] The region bounded by the curve $C$, the tangent found in part (ii) and the $x$-axis is denoted by $R$. Find the numerical value of the area of $R$.[3]

Accepted Answer

(ii)$-\frac{4}{3}x+\frac{11}{3}-2\ln 1.5$ (iv)0.88276 units$^2$

2024 RVHS H1 Q4

2024 RVHS H1 Q4