5. Let $f$ and $g$ be the functions defined by $f ( x ) = \frac { 1 } { x }$ and $g ( x ) = \frac { 4 x } { 1 + 4 x ^ { 2 } }$, for all $x > 0$. (a) Find the absolute maximum value of $g$ on the open interval $( 0 , \infty )$ if the maximum exists. Find the absolute minimum value of $g$ on the open interval $( 0 , \infty )$ if the minimum exists. Justify your answers. (b) Find the area of the unbounded region in the first quadrant to the right of the vertical line $x = 1$, below the graph of $f$, and above the graph of $g$.
5. Let $f$ and $g$ be the functions defined by $f ( x ) = \frac { 1 } { x }$ and $g ( x ) = \frac { 4 x } { 1 + 4 x ^ { 2 } }$, for all $x > 0$.\\
(a) Find the absolute maximum value of $g$ on the open interval $( 0 , \infty )$ if the maximum exists. Find the absolute minimum value of $g$ on the open interval $( 0 , \infty )$ if the minimum exists. Justify your answers.\\
(b) Find the area of the unbounded region in the first quadrant to the right of the vertical line $x = 1$, below the graph of $f$, and above the graph of $g$.\\