Question

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

Short answer

From the graphs, we observe that as degree of x increases in$y=x^k\sin x,x>0$, the curve expanded in the y-axis.

Step-by-step solution

Step 1. Given information

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

Step 2. Graph

Graph the component functions in the coordinate system,

and

Step 3. Explanation

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.

Step 4. Graph

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.

From the above graph, we observe that as the degree of x increases in $y=x^k\sin x$, the curve stretched in the $y$-axis.