Chapter 3.1, Problem 50E

a.

To determine

Draw the graph of the function .

Explanation of Solution

Given:

It is given in the question that the function is $g(x)=\frac{8}{1+e^{-0.5/x}}$ .

Graph:

  

Interpretation: In this,the red colour represents the graph of the function $g(x)=\frac{8}{1+e^{-0.5/x}}$ .

In the graph , just put the function on it,it gives the required graph.

b.

To determine

Find the asymptotes numerically from the function .

Answer to Problem 50E

The asymptotes for the function are $y=4$ .

Explanation of Solution

Given:

It is given in the question that the function is $g(x)=\frac{8}{1+e^{-0.5/x}}$ .

Concept Used:

In this,use the concept of asymptotes,there are two types of asymptotes:vertical asymptotes and horizontal asymptotes.

Calculation:

Horizontal asymptotes: $y=c$ is the horizontal asymptotes for $x\to \infty$ .

As seen from the graph, two horizontal asymptotes is

for $x\to +\infty ,y=\frac{8}{1+e^{-0.5/(\infty )}}\Rightarrow y=\frac{8}{1+e^0}\Rightarrow y=\frac{8}{1+1}=4$

  $x\to -\infty ,y=\frac{8}{1+e^{-0.5/(-\infty )}}\Rightarrow y=\frac{8}{1+e^0}\Rightarrow y=\frac{8}{1+1}=4$

So , the asymptotes are $y=4,y=4$ .

Conclusion:

The asymptotes is $y=4$ .