Chapter 4.6, Problem 4E

To determine

To fill: the blank of the given statement.

Answer to Problem 4E

For the function given by $f\left(x\right)=g\left(x\right)\cdot \sin x$ , $g\left(x\right)$ is called the damping factor of the function $f\left(x\right)$ .

Explanation of Solution

Given information:

Given statement

For the function $f\left(x\right)=g\left(x\right)\cdot \sin x$ , $g\left(x\right)$ is called the --------factor.

Calculation:

We know that, when the function $f\left(x\right)$ is given as a product of two functions, such that one of the functions is a trigonometric function, then the other function is known as the damping factor of the function.

For example;

We have a function,

  $f\left(x\right)=x^2\sin x$

So, in the case $x^2$ is the damping factor of the function $f\left(x\right)$ .

Therefore,

For the function given by $f\left(x\right)=g\left(x\right)\cdot \sin x$ , $g\left(x\right)$ is called the damping factor of the function $f\left(x\right)$ .