Show that the following can be ordered from smallest to largest for all x > 1 . Describe the method you used and state the correct order.
\[1, x, \sqrt{x}, \frac{1}{x}, \frac{1}{\sqrt{x}}\]
Let x = 4
x > sqrt (x) 1/x = 1/4 1/sqrt (x) = 1/sqrt (4) =1/2
4 > sqrt (4)
4 > 2
So....from least to greatest we have
1/x , 1/sqrt (x) , 1 , sqrt (x) , x
