Chapter 3.2, Problem 127E

(a).

To determine

To complete: the given table for the function $f(x)=(\ln x)/x$ using a graphing utility.

Answer to Problem 127E

  

Explanation of Solution

Given:

The table:

  

The function:

  $f(x)=(\ln x)/x$

Calculation:

As per the given problem

Use graphing utility to complete the table.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression, $f(x)=(\ln x)/x$ , which is required to graph.

Step 4: Press GRAPH button to graph the functions.

The table:

  

ii.

To determine

To infer: the value of f (x) as x increases without bound, using the table from part (a).

Confirm the result using graphing utility.

Answer to Problem 127E

As x increases without bound, f (x) approaches zero.

The graph:

  

Explanation of Solution

Given:

The table as obtained in part (a).

  

As per the given problem

Consider the given table of data.

For $x={10}^4$ , $f(x)=0.001$ , and

For $x={10}^6$ , $f(x)=0$

Therefore, as x increases without bound, f (x) approaches zero.

Use graphing utility to confirm the result.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression, $f(x)=(\ln x)/x$ , which is required to graph.

Step 4: Press GRAPH button to graph the functions.

The graph: