Differentiate $\ln(5ax + 4x^2)$ with respect to $x$, where $a$ is a constant. The diagram

Question

Differentiate $\ln(5ax + 4x^2)$ with respect to $x$, where $a$ is a constant. The diagram shows the curve $C$ with equation $y = 2\mathrm{e}^{2x} + 1$. Without using a calculator, find the equation of the tangent to $C$ at the point where $x = 1$, giving your answer in the form of $y = mx + c$, where $m$ and $c$ are constants. Find the exact area of the region bounded by $C$, the tangent found in part (b)(i) and the vertical line that cuts $C$ at the point where $y = 2\mathrm{e}^2 + 1$.

Accepted Answer

(a)$\frac{5a+8x}{5ax+4x^2}$ (b)(i)$y=4x+3$ (b)(ii)$e^2-5$

2024 EJC H1 Q4

2024 EJC H1 Q4