The graph shows a rough representation of the (aggregate) market depth† 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). A graph has horizontal axis labeled t from 9.5 to 16 and vertical axis labeled m(t) from 10 to 100. A function with 2 parts is graphed. The first part enters the window at (9.5, 66), goes horizontally right, and stops at the open point (14.75, 66). The second part begins at the closed point (14.75, 10), goes up and right, sharply changes direction, goes up and right more steep, and ends at the point (16, 100). (a) Compute the following. (If a limit does not exist, enter DNE, and say why.) lim t→14.75− m(t) = The limit does exist. The limit does not exist because it diverges. The limit does not exist because the limit from the left does not match the limit from the right. lim t→14.75+ m(t) = The limit does exist. The limit does not exist because it diverges. The limit does not exist because the limit from the left does not match the limit from the right. lim t→14.75 m(t) = The limit does exist. The limit does not exist because it diverges. The limit does not exist because the limit from the left does not match the limit from the right. m(14.75) = (b) What do the answers to part (a) tell you about the market depth? Just prior to 2:45 pm, the S&P market depth was approaching million shares, but then fell suddenly to million shares at 2:45 exactly, then immediately following 2:45 it began to recover at values close to million share
The graph shows a rough representation of the (aggregate) market depth† 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).
A graph has horizontal axis labeled t from 9.5 to 16 and vertical axis labeled m(t) from 10 to 100. A function with 2 parts is graphed.
- The first part enters the window at (9.5, 66), goes horizontally right, and stops at the open point (14.75, 66).
- The second part begins at the closed point (14.75, 10), goes up and right, sharply changes direction, goes up and right more steep, and ends at the point (16, 100).
(a)
Compute the following. (If a limit does not exist, enter DNE, and say why.)
lim
t→14.75−
m(t) =
The limit does exist.
The limit does not exist because it diverges.
The limit does not exist because the limit from the left does not match the limit from the right.
lim
t→14.75+
m(t) =
The limit does exist.
The limit does not exist because it diverges.
The limit does not exist because the limit from the left does not match the limit from the right.
lim
t→14.75
m(t) =
The limit does exist.
The limit does not exist because it diverges.
The limit does not exist because the limit from the left does not match the limit from the right.
m(14.75) =
(b)
What do the answers to part (a) tell you about the market depth?
Just prior to 2:45 pm, the S&P market depth was approaching million shares, but then fell suddenly to million shares at 2:45 exactly, then immediately following 2:45 it began to recover at values close to million shares.
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