Analysis and Approaches for IBDP Maths Ebook 2 | Page 273

Quick Practice
You are asked to investigate the areas above or below the curve
defined rectangles.
y� e �x restricted in
The figure shows the graph of g( x)
� e �x . A , C and F are three distinct points on the
graph of f such that the x -coordinates of A , C and F are 1, 2 and 3 respectively. AB ,
DCE and GF are horizontal lines. AD , BCG and EF are vertical lines.
Part I – Investigating the Quantity 1
Let
A
k
be the area bounded by the graph of g , the line x
� k and the line y �g( k � 1) .
20
Consider the rectangle ABCD .
(a) (1) Find the area of the rectangle ABCD .
(2) Find the area of the triangle ACD .
(3) Hence, write down an inequality for A
1.
(b) (1) Find the area of the triangle CFG .
(2) Hence, suggest an inequality for A
2
.
(c) Find an inequality for A
3
.
(d) Find an inequality for A
n
.
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