CPM Homework Help : PC Problem 7-31

Write the sum for estimating $A(\frac { 4 } { x }, 1 ≤ x ≤ 4)$ using $10$ left-endpoint rectangles. Determine if the estimate is an upper bound or lower bound. Justify your answer with a sketch of the curve showing a typical rectangle.

Hint:

$1. \text{ width}=\frac{\text{length of interval}}{\text{# of rectangles}}$

2. height $= f\left(x\right)$

3. inside function $= \left(\text{width}\right)\left(x + \text{start}\right)$

$\text{Width}\displaystyle \sum_{k =\text{ start}-1}^{\text{end}}\frac{4}{(\text{(width)}(x+\text{start}))}$

First quadrant curve, x axis scaled in tenths, from 0 to 5, concave up curve with approximate points at (1, comma 4), (1.9, comma 2), (2.8, comma 1.5), 10 vertical bars, left starting at 1, each width of 0.3, with top left vertex of each bar on the curve.