Airline Stocks Prior to the September 11, 2001 attacks, United Airlines st...

Airline Stocks Prior to the September 11, 2001 attacks, United Airlines stock was trading at around $35 per share. Immediately following the attacks, the share price dropped by $15. Let U(t) be this cost at time t, and take t 11 to represent September 11, 2001. What does the given information tell you about HINT [See Example 4(b).]

Example 4(b):

The graph of a function f is shown in Figure 1. (Recall that the solid dots indicate points on the graph, and the hollow dots indicate points not on the graph.)

From the graph, analyze the following limits.

b. This time we move our pencil point toward x = 0. Referring to Figure 4, if we start from the left of x = 0 and approach 0 (by moving right), the y-coordinate approaches −1. However, if we start from the right of x = 0 and approach 0 (by moving left), the y-coordinate approaches 3. Thus (see Example 2),

Because these limits are not equal, we conclude that

In this case there is a “break” in the graph at x = 0, and we say that the function is discontinuous at x = 0. (See Section 3.2.)