BuyFind

Precalculus: Mathematics for Calcu...

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

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

Answer to Problem 83E

The completed table is as shown:

    x1x
    11
    20.5
    100.3333
    1000.01
    10000.001
    1.01
    0.52
    0.110
    0.01100
    0.0011000

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

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.1, Problem 83E

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.

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