   Chapter 4.5, Problem 54E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Numerical, Graphical, and Analytic AnalysisIn Exercises 53-56, use a graphing utility to complete the table and estimate the limit as x approaches infinity. Then use a graphing utility to graph the function and estimate the limit. Finally. Find the limit analytically and compare your results with the estimates. x 10° 101 102 103 104 105 106 f(x) f ( x ) = x 2 − x x ( x − 1 )

To determine

To calculate: The limit of the provided expression f(x)=x2xx(x1) at infinity using the tabular method, graphically and analytically.

Explanation

Given:

The expression f(x)=x2xx(x1) and the table,

x100101102103104105106f(x)

Formula used:

The following limits hold:

limx1xr=0,r>0limx1xr=0,r>0

Calculation:

The provided table can be completed with the help of the Ti-83 calculator.

The first entry in the second row would be,

f(100)=(100)2(100)(100)((100)1)

Enter this in the calculator to obtain:

f(100)=1

Proceed similarly to obtain the remaining values. This gives the complete table as:

x100101102103104105106f(x)15.131750.1256500.1255000.12550000.125500000.125

This implies that,

limx(x2xx(x1))=

Graph:

This can be verified using the graphical method.

This can be verified by plotting the graph of the provided expression using the Ti-83 calculator.

Proceed as follows:

Step 1: Press the [Y=] key.

Step 2: To the right of Y1, enter the expression provided.

Step 3: Press [WINDOW] and enter 1000 for Xmin, 100 for Xmax, 0 for Ymin and 100 for Ymax.

Step 5: Press [GRAPH].

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 