Chapter 7.7, Problem 60HP

To determine

To find: whether $x>Inx$ is sometimes, always or never true.

Answer to Problem 60HP

The given function is always true for the given value.

Explanation of Solution

Given information:

The function is $x>Inx$ .

Graph:

Consider the function

  $y=x-Inx,x>0$

Graph the function is shown below:

  

Graph $\left(1\right)$

From the graph it is clear that for all $x>0$ , $y>0$

That is,

  $x-Inx>0$

  $x>Inx$

Therefore for all values of $x>0$ , $x>Inx$ .