Chapter 1: Q. 20 (page 87)

Use a calculator or other graphing utility to investigate the graph $f (x) = x \sin (\frac{1}{x})$ near x = 0. Be sure to have your calculator set to radian mode. Use the graphs to make an educated guess for $lim_{x \to 0} f (x)$ .

Short Answer

Expert verified

f(x) is undefined near x=0

Step by step solution

Step 1. Given information.

We have been given a function $f (x) = x \sin (\frac{1}{x})$ .

We have to use a calculator or other graphing utility to investigate the graph of the function near x = 0.

Step 2. Graph the function

Function is :

$f (x) = x \sin (\frac{1}{x})$

The graph is :

We can see that at x=0 is not defined.

Step 3. Solving the limit expression.

Solving the limit expression,

$\begin{aligned} lim_{x \to 0} f (x) = lim_{x \to 0} x \sin (\frac{1}{x}) \\ = 0 \sin (\frac{1}{0}) \\ = 0 \sin (\infty) \end{aligned}$

= undefined

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Use a calculator or other graphing utility to investigate the graph $f (x) = x \sin (\frac{1}{x})$ near x = 0. Be sure to have your calculator set to radian mode. Use the graphs to make an educated guess for $lim_{x \to 0} f (x)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Graph the function

Step 3. Solving the limit expression.

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Use a calculator or other graphing utility to investigate the graph f(x)=xsin1xnear x = 0. Be sure to have your calculator set to radian mode. Use the graphs to make an educated guess forlimx→0 f(x).

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Graph the function

Step 3. Solving the limit expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use a calculator or other graphing utility to investigate the graph $f (x) = x \sin (\frac{1}{x})$ near x = 0. Be sure to have your calculator set to radian mode. Use the graphs to make an educated guess for $lim_{x \to 0} f (x)$ .