CPM Homework Help : PC3 Problem 9-40

Write and evaluate the sum for approximating $A(\frac{4}{x},1\le x\le4)$ using $10$ left endpoint rectangles. Determine if the approximation is an overestimate or an underestimate. Justify your answer with a sketch of the curve showing a typical rectangle.

Step1:

$\text{ width}=\frac{4-1}{10}=0.3$

Step 2:

$x_{0} = 1, x_{1} = 1.3, x_{2} = 1.6, ...$
Write an equation for $x_{n}$ .

Step 3:

$\text{area}\approx 0.3 \displaystyle \sum_{n=0}^{9}\frac{4}{x_n}$