Question

Notation: Describe the meanings of each of the following mathematical expressions or how they are commonly used in this chapter:

$f\left({x_k}^{\ast }\right)∆x$

Short answer

The expression$f\left({x_k}^{\ast }\right)∆x$ is the area of kthrectangle.

Where$f\left({x_k}^{\ast }\right)$ is the height and$∆x$ is the width of the rectangle.

Step-by-step solution

Step 1. Given information.    

We are given an expression,

$f\left({x_k}^{\ast }\right)∆x$

Step 2. Defining the expression 

In Riemann Sums, the expression$f\left({x_k}^{\ast }\right)∆x$ is the area ofkthrectangle.

Where$f\left({x_k}^{\ast }\right)$ is the height and$∆x$ is the width.