Chapter 6.2, Problem 77E

a.

To determine

To sketch: The graph of the functions are $f\left(x\right)=x^n$ and $g\left(x\right)=x^{\frac{1}{n}}$ for n = 2,3,4 and $x>0$.

b.

To determine

To find: The geometric interpretation of the area function $A_n\left(x\right)={\displaystyle \underset{0}{\overset{x}{\int }}\left(f\left(s\right)-g\left(s\right)\right)ds}$ for n = 2,3,4,… and $x>0$.

c.

To determine

To find: The positive root of $A_n\left(x\right)=0$ in terms of n and find it’s changes with n.