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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Flash Crash The graph shows a rough representation of the (aggregate) market depth11 of the stocks comprising the S&P 500 on the day of the U.S. stock market crash at 2:45 pm on May 6, 2010, the “Flash Crash” (t is the time of the day in hours, and m ( t ) is the market depth in millions of shares).

images

a. Compute the following (if a limit does not exist, say why):

lim t 14.75 m ( t ) ,

lim t 14.75 + m ( t ) ,

lim t 14.75 m ( t ) ,

m ( 14.75 ) .

b. What do the answers to part (a) tell you about the market depth?

(a)

To determine

The value of limt14.75m(t), limt14.75+m(t), limt14.75m(t) and m(14.75) using the graph which is as follows:

images

Explanation

Given information:

The graph is as follows:

In graph, t is the time of the day in hours and m(t) is the market depth in millions of shares. The above graph represents the condition of the market depth of the stocks comprising the S&P 500 during the U.S. stock market crash which occurs on May 6,2010 at 2:45 pm.

From the graph, evaluate the limit for t tends to 14.75 for the function m(t).

As x is approaching 14.75 from the left, m(t) appears to approach the open dot at the height of 66.

Thus, it is concluded from the graph that on approaching 14.75 from the left side, m(t) appears to be approaching 66 which means limt14.75m(t)=66.

Then, evaluate the limit for t tends to 14.75+ for the function m(t)

(b)

To determine

The interpretation about the market depth according to the value of limt14.75m(t), limt14.75+m(t) and m(14.75) is 66, 10 and 10 while the provided limit limt14.75m(t) does not exist.

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