A curve $C$ has equation $y=1+\frac{1}{1+2x}$. Without using a calculator, find the equation of

Question

A curve $C$ has equation $y=1+\frac{1}{1+2x}$. Without using a calculator, find the equation of the tangent $L$ to $C$ at the point where $x=0$, giving your answer in the form $y=mx+c$, where $m$ and $c$ are constants.[3] Sketch the graphs of $C$ and $L$ on a single diagram, stating the equations of all asymptotes and the coordinates of the points of intersection with the axes.[4] Hence, find the exact area of the finite region bounded by $C$, $L$ and the line $x=1$.[3]

Accepted Answer

(a)$y=-2x+2$ (c)$\frac{1}{2}\ln 3$

2024 YIJC H1 Q4

2024 YIJC H1 Q4