Chapter 8: Q. 57 (page 552)

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

Short Answer

Expert verified

The required graph is

Step by step solution

Step 1. Given Information

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

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 $x \to 0, \frac{\sin x}{x} \to 1$

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Graph

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Use a graphing utility to graph the function f(x)=sinxx,x>0. Based on the graph, what do you conjecture about the value of sinxxfor x close to 0?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

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