Chapter A.1, Problem 81E

a.

To determine

The complete table.

Answer to Problem 81E

The complete table shown above.

Explanation of Solution

Given:

The given table is,

$n$	$0.0001$	$0.01$	$1$	$100$	$10,000$
$\frac{5}{n}$	$n$	$n$	$n$	$n$	$100$

Calculation:

Substitute the values of n in above equation.

For $n=0.001$ ,

  $\frac{5}{0.001}=5000$

For $n=0.01$ ,

  $\frac{5}{0.01}=500$

For $n=1$ ,

  $\frac{5}{1}=5$

For $n=100$ ,

  $\frac{5}{100}=0.05$

For $n=10,000$ ,

  $\frac{5}{10,000}=0.0005$

The complete table is given below,

$n$	$0.0001$	$0.01$	$1$	$100$	$10,000$
$\frac{5}{n}$	$5000$	$500$	$5$	$0.05$	$0.0005$

Conclusion:

Hence, the complete table shown above.

b.

To determine

The conjecture about the value of $\frac{5}{n}$ ?

Answer to Problem 81E

The value of $\frac{5}{n}$ increases with the decrease in the value of n and decreases with increase in the value of n .

Explanation of Solution

Given:

The given table is,

$n$	$0.0001$	$0.01$	$1$	$100$	$10,000$
$\frac{5}{n}$	$n$	$n$	$n$	$n$	$100$

Calculation:

The complete table is,

$n$	$0.0001$	$0.01$	$1$	$100$	$10,000$
$\frac{5}{n}$	$5000$	$500$	$5$	$0.05$	$0.0005$

From above table it is observed that the value of $\frac{5}{n}$ increases with the decrease in the value of n and reaches infinity at 0. The value of $\frac{5}{n}$ decreases with increase in the value of n and reaches to 0 at infinity.

Conclusion: The value of $\frac{5}{n}$ increases with the decrease in the value of n and decreases with increase in the value of n .