Question

Use a graphing utility to graph the function $f\left(x\right)=\frac{\sin x}{x},x>0$. Based on the graph, what do you conjecture about the value of $\frac{\sin x}{x}$for x close to 0?

Short answer

The required graph is

Step-by-step solution

Step 1. Given Information

The given function is$f\left(x\right)=\frac{\sin x}{x}$

Step 2. Explanation

Graph the component functions in the coordinate system,

and

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

Step 3. Graph

Plot these points and connect them to get the graph.

From the graph, we can say that as x close to zero then function is close to one that is as$x\to 0,\frac{\sin x}{x}\to 1$