### Home > PC3 > Chapter 9 > Lesson 9.1.2 > Problem9-40

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.

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

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

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