Chapter 8.5, Problem 63AYU

To determine

To plot: The graph of the equations $y=\frac{1}{x}\sin x$ , $y=\frac{1}{x^2}\sin x$ and $y=\frac{1}{x^3}\sin x$ , and observe the pattern.

Answer to Problem 63AYU

The graph of the equation $y=\frac{1}{x}\sin x$ is periodic, $y=\frac{1}{x^2}\sin x$ is cubic and symmetric about positive and negative xy- axis, and the graph of the equation $y=\frac{1}{x^3}\sin x$ is cubic and symmetric about positive y axis.

Explanation of Solution

Given:

The equations are $y=\frac{1}{x}\sin x$ , $y=\frac{1}{x^2}\sin x$ and $y=\frac{1}{x^3}\sin x$ .

Calculation:

Plot the graph of the equation $y=\frac{1}{x}\sin x$ .

  

Plot the graph of the equation $y=\frac{1}{x^2}\sin x$ .

  

Plot the graph of the equation $y=\frac{1}{x^3}\sin x$ .

  

The graph of the equation $y=\frac{1}{x}\sin x$ is in periodic form, the graph of the equation $y=\frac{1}{x^2}\sin x$ is cubic form but symmetric about positive and negative xy- axis, and the graph of the equation $y=\frac{1}{x^3}\sin x$ is cubic and symmetric about positive y axis.