   Chapter 3.4, Problem 6E

Chapter
Section
Textbook Problem

# (a) Use a graph of f ( x ) = ( 1 − 2 x ) x to estimate the value of lim x → ∞ f ( x ) correct to two decimal places.(b) Use a table of values of f ( x ) to estimate the limit to four decimal places.

To determine

a)

To estimate:

The value of limit limx∞ f(x) correct to two decimal places

Explanation

1) Concept:

Use the definition of limit at infinity.

2) Definition:

Limit at infinity:

Let f be function defined on (a,). Then

limxf(x)=L

Means that the values of f(x) can be made arbitrarily close to L by requiring x to be sufficiently large.(means, values of f(x) approaches L as x becomes larger and larger.)

3) Given:

f(x)=1-2xx

4) Calculation:

The graph of f(x)=1-2xx as shown above

By zooming above graph,

From the graph a, as x approaches to larger values, the value of f(x) approaches to 0.13

Therefore,

limx∞ f(x)=0.13

Conclusion:

Therefore,

limx∞ f(x)=0.13

b)

To estimate:

The value of limit to four decimal places

Solution:

0.1353

1) Concept:

Use the definition of limit at infinity.

2) Definition:

Limit at infinity:

Let f be function defined on (a,). Then

limxf(x)=L

Means that the values of f(x) can be made arbitrarily close to L by requiring x to be sufficiently large.(means, values of f(x) approaches L as x becomes larger and larger

### 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 