Chapter 11.2, Problem 63E

To determine

To show:

Limit of $f$ as $t\to 2$ does not exist

Answer to Problem 63E

Hence, limit of the function does not exist at $t=2$ .

Explanation of Solution

Given information:

  $f\left(t\right)=\{\begin{array}{l}40000,0<t\le 1\\ 412001<t\le 2\\ 424362<t\le 3\end{array}$

Proof:

Consider the function that depicts the salary guaranteed by a union,

  $f\left(t\right)=\{\begin{array}{l}40000,0<t\le 1\\ 412001<t\le 2\\ 424362<t\le 3\end{array}$

For checking the existence of limit as $t$ approaches $2$ , to find the value of function as $t$ approaches $2$ from left to right.

Where, $t=1.9$

  $f\left(t\right)=40000$

Where, $t=1.99$

  $f\left(t\right)=40000$

Where, $t=1.999$

  $f\left(t\right)=40000$

Where, $t=2$

  $f\left(t\right)=40000$

Where, $t=2.001$

  $f\left(t\right)=42436$

Where, $t=2.01$

  $f\left(t\right)=42436$

Where, $t=2.1$

  $f\left(t\right)=42436$

As the value of function approaches two different values at $t$ approaches $2$ from left and right, the limit of the function does not exist at $t=2$ .