The diagram shows part of the graph of $y=\ln x$ with $n$ rectangles of equal width, where $n$ is a

Question

The diagram shows part of the graph of $y=\ln x$ with $n$ rectangles of equal width, where $n$ is a positive integer. Show that the total area of the $n$ rectangles, $A$, is Evaluate $\underset{n	o \infty }{\mathop{\lim }}\,A$, giving your answer correct to $4$ decimal places.[2] It is given that $\mathrm{f}\left( x ight)=\frac{a}{{{x}^{2}}}+bx+c$, where $a$, $b$ and $c$ are constants. The curve with equation $y=\mathrm{f}\left( x ight)$ has a minimum point with coordinates $\left( 1,2 ight)$ and $\displaystyle\int_{1}^{3}{\mathrm{f}\left( x ight)}\,\mathrm{d}x=\frac{20}{3}$. Find the equation of the curve.[4]

Accepted Answer

(a)(ii) $\lim_{n 	o \infty} A = 0.3863$ units² (b) $f(x) = \dfrac{1}{x^2} + 2x - 1$

2021 YIJC P1 Q1

2021 YIJC P1 Q1

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