Use a graphing utility to graph$y=\frac{1}{x}\sin x,y=\frac{1}{x^2}\sin x,y=\frac{1}{x^3}\sin xforx>0$. What patterns do you observe?

The given functions are$y=\frac{1}{x}\sin x,y=\frac{1}{x^2}\sin x,y=\frac{1}{x^3}\sin xforx>0$

Graph the component functions in the coordinate system,

Now, select several values of x at which we can compute the different values of y, The table shows the computation as follows,

Plot these points and connect them to get the graph of the function.

Next, select several values of x at which we can compute the different values of y, The table shows the computation as follows,

Plot these points and connect them to get the graph of the function.

Select several values of x at which we can compute the different values of y, The table shows the computation as follows,

Plot these points and connect them to get the graph of the function.

From the above graph, we observe that as the degree of x increases in $y=\frac{\sin x}{x^k},x>0$the curve compressed in the x-axis.