Chapter 6.3, Problem 72E

To determine

(a)

To find: We have to compare the rate of growth of $f\left(x\right)=x^{0.1}$ and $g\left(x\right)=\ln x$ by graphing both of the functions in different viewing rectangles. We also find the value of x, when the function f finally surpass the graph of g.

To determine

(b)

To find: We have to graph the function $h\left(x\right)=\frac{\ln x}{x^{0.1}}$ in a viewing rectangle that displays the behavior of the function as $x\to \infty$.

To determine

(c)

To find: We have to find the number N such that if $x<N$ then $\frac{\ln x}{x^{0.1}}<0.1$.