CPM Homework Help : PC3 Problem 8-91

Approximate $A\left(\frac{1}{x},1\le x\le5\right)$ using eight left endpoint rectangles. Use sigma notation to show the sum of the areas of the rectangles.

Step 1:

Determine the width of each rectangle.

Answer 1:

$\frac{\text{length of interval}}{\text{number of rectangles}}$

Step 2:

Write an equation for the $x_{n}s$ .

Hint:

$x_{0} = 1$ , $x_{1} = 1.5$ , ...

Step 3:

Use sigma notation to show the sum of the areas of the $8$ rectangles.

Answer 2:

width $\displaystyle\sum_{n=0}^{7}\frac{1}{\text{(expression for }x_n\text{s})}$