Chapter 4.3, Problem 79E

To determine

To calculate: compare rates of growth of the function $f\left(x\right)=Inx$ and $g\left(x\right)=\sqrt{x}$ by the drawing their graph on a common screen using the viewing rectangle $\left[-1,30\right]by\left[-1,6\right]$ .

Explanation of Solution

Given information:

The $f\left(x\right)=Inx$ and $g\left(x\right)=\sqrt{x}$ by the drawing their graph on a common screen using the viewing rectangle $\left[-1,30\right]by\left[-1,6\right]$ .

Formula used:

Slope of the graph shows the right position of the function two provided points.

1^st take the equation and solve it for x. it means replace the points x and y.

Simplify the given function.

Then find the value of y in terms of x.

Calculation:

  $f\left(x\right)=Inx$ and $g\left(x\right)=\sqrt{x}$ by the drawing their graph on a common screen using the viewing rectangle $\left[-1,30\right]by\left[-1,6\right]$ .

  $\begin{array}{l}f\left(x\right)=In\left(x\right)\\ y=Iny\end{array}$

Solve the expression ,

  $\begin{array}{l}y=inx\\ here\left(g\left(x\right)\right)=\sqrt{x}\\ g\left(x\right)=x^{\frac{1}{2}}\\ y=y^{\frac{1}{2}}\end{array}$

From the two functions the rate of growth starts from x=0 and get up with increases x but the function $g\left(x\right)=\sqrt{x}$ has more growth with the y-axis increases.

The graph of the given function $g\left(x\right)=\sqrt{x}$ ,

  $\begin{array}{l}f\left(x\right)=In\left(x\right)\\ y=Iny\end{array}$

  

Thus, no further explanation are here.

This is the required answer.