# the tables and to find the size of the fraction 1 x as x gets large and small. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.1, Problem 83E
To determine

## To complete: the tables and to find the size of the fraction 1x as x gets large and small.

Expert Solution

The completed table is as shown:

 x 1x 1 1 2 0.5 10 0.3333 100 0.01 1000 0.001 1.0 1 0.5 2 0.1 10 0.01 100 0.001 1000

As x increases, the k term will be greater than the k+1 term

Or, as x increases, 1x decreases.

### Explanation of Solution

Given information:

Given table Calculation:

When x=1,1x=1

x=2,1x=12=0.5x=3,1x=0.3333...x=4,1x=0.25

In general, when x=k,1x=1k and x=k+1,1x=1(k+1)

1k1k+1=1k(k+1)becausekisapositiverealnumber

k(k+1) is a positive integer and so 1k(k+1) is a positive real number

That is,

1k1k+1>01k>1k+1

As x increases, the k term will be greater than the k+1 term

Or, as x increases, 1x decreases.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!