Chapter 11.1, Problem 77E

(a)

To determine

To graph:

The limit that is possible of the to reach and one that is not possible to reach a graphing utility

Explanation of Solution

Given information:

Limit that is possible to reach and one that is not possible to reach

Graph:

  

Graph 1: Limit can be reaches

  

Graph 2: Limit cannot be reaches

Interpretation:

Consider, the followings equations as:

1. Limit can be reaches:

$\underset{x\to -1}{\lim }\left(2x^2+x-4\right)$

2. Limit cannot be reaches:

  $\underset{x\to -2}{\lim }\frac{x-2}{2x^2-x-2}$

The graph of the first equation:

  

The graph of the second equation:

  

The graph of the both functions shows that the function is continuous around $x=-1$ and the second equation is continuous around $x=2$ . Thus both eqns. should be reached.

(b)

To determine

To graph:

The function to reach and one that is not possible to reach using a decimal setting

Explanation of Solution

Given information:

Limit that is possible to reach and one that is not possible to reach

Graph:

  

Graph 1: Limit can be reaches

  

Graph 2: Limit cannot be reaches

Interpretation:

Consider, the followings equations as:

1. Limit can be reaches:

$\underset{x\to -1}{\lim }\left(2x^2+x-4\right)$

2. Limit cannot be reaches:

  $\underset{x\to -2}{\lim }\frac{x-2}{2x^2-x-2}$

The graph of the first equation:

  

The graph of the second equation:

  

The limit of the first equation is $x=1$ can be reached while the limit for the second function in $x=2$ cannot as the second function has a hole in the graph for $x=2$