The curve $C$ has equation $$y = \frac{2}{\mathrm{e}^{1-2x}} - \frac{1}{(2x+1)^2}.$$ Without using

Question

The curve $C$ has equation $$y = \frac{2}{\mathrm{e}^{1-2x}} - \frac{1}{(2x+1)^2}.$$ Without using a calculator, find the equation of the tangent to $C$ at the point where $x = \frac{1}{2}$, giving your answer in the form $y = mx + c$, where $m$ and $c$ are constants.[5] The tangent found in part (a) meets the $y$-axis at $A$ and the $x$-axis at $B$. Find the exact area of triangle $AOB$, where $O$ is the origin. [3]

Accepted Answer

(a)$y=\frac{9}{2}x-\frac{1}{2}$ (b)area of $\triangle AOB=\frac{1}{36}$

2024 RI H1 Q3

2024 RI H1 Q3

Solution:

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