Chapter 4.3, Problem 80E

a.

To determine

To define: to draw the graphs of the functions $f\left(x\right)=1+In\left(1+x\right)$ and $g\left(x\right)=\sqrt{x}$ in a suitable viewing rectangle viewing .if even when a logarithmic function starts out higher than a root function . can it is overtaken ultimately by the root function.

Answer to Problem 80E

As according see the picture the blue curve the square root function will eventually take the red curve of logarithmic function.

  

Explanation of Solution

Given information:

The term $f\left(x\right)=1+In\left(1+x\right)$ and $g\left(x\right)=\sqrt{x}$ in a suitable viewing rectangle viewing .if even when a logarithmic function starts out higher than a root function . can it is overtaken ultimately by the root function.

The function $f\left(x\right)=1+In\left(1+x\right)$ and $g\left(x\right)=\sqrt{x}$ in a suitable viewing rectangle viewing .if even when a logarithmic function starts out higher than a root function . can it is overtaken ultimately by the root function.

As the picture given below the blue curve square root function will eventually overtake the red curve logarithmic function.

  

This is the graphing calculation in the viewing graphing window $\left[-7,31\right]by\left[-4,8\right]$

b.

To determine

To define: The rounded of two decimal places , the solutions of the equations $\sqrt{x}=1+In\left(1+x\right)$ .

Answer to Problem 80E

In the graph the it is obvious form the picture above that the graphs of two functions

  

  $x\approx 13.50$

Explanation of Solution

Given information:

The rounded of two decimal places , the solutions of the equations $\sqrt{x}=1+In\left(1+x\right)$ .

The function . $\begin{array}{l}\sqrt{x}=1+In\left(1+x\right)\\ x^{\frac{1}{2}}=1+In1+Inx\end{array}$ .

In the graph the it is obvious form the picture above that the graphs of two functions

  

  $x\approx 13.50$

The two functions f and g intersects at the point $\left(13.499,3.674\right)$

The solution of the give equation rounded to two decimal is $x\approx 13.50$