The curve $C$ has equation $y = \ln(k - 2x)$ where $k$ is a negative constant. Sketch the

Question

The curve $C$ has equation $y = \ln(k - 2x)$ where $k$ is a negative constant. Sketch the graph of $C$, stating, in terms of $k$, the coordinates of any point(s) of intersection with the axes and the equation of any asymptote(s).[2] It is given now that $k = -3$. The equation of the tangent to $C$ at $x = -\frac{5}{2}$ cuts the $x$-axis and the $y$-axis at point $P$ and point $Q$ respectively. Find the exact area of the triangle $OPQ$.[4]

Accepted Answer

(b)Area of $\triangle POQ$ =$\frac{1}{2}(\frac{5}{2}-\ln 2)^2$ units$^2$

2024 VJC H1 Q3

2024 VJC H1 Q3