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) $L:y=-2x+2$. (b) Sketch shown; C asymptotes $x=-\dfrac12$, $y=1$. (c) $\dfrac12\ln3$ square units.

2024 YIJC H1 Q4

2024 YIJC H1 Q4

Solution:

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