Chapter 12.1, Problem 67E

a.

To determine

To find: To find the graph in standard viewing window reveal the possibility to reach the limit.

Answer to Problem 67E

No, the graph in standard viewing window does not reveal the possibility to reach the limit.

Explanation of Solution

Given: From the exercises $5-10$ the functions are,

  $\underset{x\to -1}{\lim }\left(2x^2+x-4\right)$ -can reach the limit.

  $\underset{x\to -2}{\lim }\frac{x-2}{x^2-x-2}$ -cannot reach the limit.

Graphing the limits in a standard window using graphing utility,

  

The first function is continuous at $x=-1$ and the second function is continuous at $x=2$ .

From the graphs we can understand that the graphing using standard window does not reveal the possibility of reaching the limits.

b.

To determine

To find: To find the graph in decimal setting gives the possibility to reach the limit.

Answer to Problem 67E

Yes, the graph in decimal setting does reveal the possibility to reach the limit.

Explanation of Solution

Given: From the exercises $5-10$ the functions are,

  $\underset{x\to -1}{\lim }\left(2x^2+x-4\right)$ -can reach the limit.

  $\underset{x\to -2}{\lim }\frac{x-2}{x^2-x-2}$ -cannot reach the limit.

Graphing the limits in a decimal setting using graphing utility,

  

The first function $x=-1$ can be reached but the second function $x=2$ cannot reach because it has a hole in it.

From the graphs we can understand that the graphing using decimal setting does reveal the possibility of reaching the limits.