   Chapter 2.3, Problem 33E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) Estimate the value of lim x → 0 x 1 + 3 x − 1 by graphing the function f ( x ) = x / ( 1 + 3 x − 1 ) .(b) Make a table of values of f(x) for x close to 0 and guess the value of the limit.(c) Use the Limit Laws to prove that your guess in correct.

(a)

To determine

To estimate: The value of the function when x approaches zero by graphing the function f(x).

Explanation

Given:

The graph of the function f(x)=x1+3x1.

Draw the graph of the function f(x)=x1+3x1 by using the graphing calculator as shown below in Figure 1.

From the graph, as x=0, then f(x) is not defined. But x approaches 0, then f(x) goes to 23

(b)

To determine

To guess: The value of the limit by using the table of values of f(x) for x close to 0.

(c)

To determine

To prove: The limit value of the function is 23.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 