The graph of $y=e^{1-x}$ for $0\leq x\leq1$, is shown in the diagram below. $n$ rectangle

Question

The graph of $y=e^{1-x}$ for $0\leq x\leq1$, is shown in the diagram below. $n$ rectangles of equal width are drawn as shown in the interval between $x=0$ and $x=1$. The area of these rectangles, $A$, is used to estimate $B$ which is the area bounded by $y=e^{1-x}$, $x$-axis, $y$-axis and the line $x=1$. Show that $A=\dfrac{e-1}{n\left(e^{\frac{1}{n}}-1\right)}$.[3] Find $B$ in terms of $e$. Hence find the least value of $n$ such that $A$ exceeds $95\%$ of $B$.[5]

Accepted Answer

(a) $A=\dfrac{e-1}{n(e^{\frac{1}{n}}-1)}$ (b) $B=e-1$, least $n=10$.

2026 HCI Promo Q7

2026 HCI Promo Q7

Solution:

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