Limit - Stock Price Word Problem

[hopelynnwelch]

So I have this on a quiz and the answer is that the limit DNE. I am trying to reason why this is the answer...

I am thinking the reason this limit DNE is because of the information given? I know that the stock was at 33 dollars and that it moved in a negative direction 14 dollars, but I don't how the stock moved in the positive direction. Meaning I don't know if it was ever more than 33 dollars. Does this mean that because I can't evaluate it from both directions the limit DNE?

If it asked me what was the limit as t approaches 11 from the negative side, then a limit would exist?

Here is the problem:

Prior to the September 11, 2001 attacks, an airline's stock was trading at around $33 per share. Immediately following the attacks, the share price dropped by $14.00. 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 aboutlim t→11 U(t)?

Answer: DNE

 

[stapel]

So I have this on a quiz and the answer is that the limit DNE. I am trying to reason why this is the answer...

Prior to the September 11, 2001 attacks, an airline's stock was trading at around $33 per share. Immediately following the attacks, the share price dropped by $14.00. 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 aboutlim t→11 U(t)?

Answer: DNE

Do a rough graph. Yes, you don't know what the stock price was, exactly, in the middle term before and after. You have no idea what the stock was, even roughly, in the long term before and after. But you don't care about that. The limit only looks at what the y-values are close to the target x-value. In other words, you only area what the values were in the very-short term before and after.

You know that the trend-line had been fairly consistently around y = 33. So draw at line wiggling around a bit, but then smoothing out to y = 33 as it approaches t = 11 from the left:

graph:
          ^ y
          |
_---_-----o
          |
          |
          |
          |
          |
          |
--|---|---|---|---|---|--> t
  9  10  11  12  13  14

Immediately after (and that "immediately" is crucial), the y-value was at y = 14. And the stock took quite a while even to begin to recover. So draw a line leaving t = 11 at a height of y = 14:

graph:
          ^ y
          |
_---_-----o
          |
          |
          |
          o-_   _ ___-_  _
          |  --- -     --
          |
--|---|---|---|---|---|--> t
  9  10  11  12  13  14

Remember that "the" limit value is the value of the limit if that value is the same from both sides. What could possibly be the limit value, at t = 11, on this graph?

 

[hopelynnwelch]

Do a rough graph. Yes, you don't know what the stock price was, exactly, in the middle term before and after. You have no idea what the stock was, even roughly, in the long term before and after. But you don't care about that. The limit only looks at what the y-values are close to the target x-value. In other words, you only area what the values were in the very-short term before and after.

You know that the trend-line had been fairly consistently around y = 33. So draw at line wiggling around a bit, but then smoothing out to y = 33 as it approaches t = 11 from the left:

graph:
          ^ y
          |
_---_-----o
          |
          |
          |
          |
          |
          |
--|---|---|---|---|---|--> t
  9  10  11  12  13  14

Immediately after (and that "immediately" is crucial), the y-value was at y = 14. And the stock took quite a while even to begin to recover. So draw a line leaving t = 11 at a height of y = 14:

graph:
          ^ y
          |
_---_-----o
          |
          |
          |
          o-_   _ ___-_  _
          |  --- -     --
          |
--|---|---|---|---|---|--> t
  9  10  11  12  13  14

Remember that "the" limit value is the value of the limit if that value is the same from both sides. What could possibly be the limit value, at t = 11, on this graph?

At t=11 the limit would also be DNE because you can't evaluate it from both sides either? I see what you are saying about how the key word is instantaneously. Any time I see graphs like this I know a limit DNE but in my mind I was picturing a sharp drop in price and not as you graphed it. That was very helpful! Thank you!

 

[stapel]

At t=11 the limit would also be DNE because you can't evaluate it from both sides either?

What "it" are you trying to "evaluate"?

The point is that the value clearly "ought" to be one thing as you approach t = 11 from the left, but equally-clearly "ought" to be an entirely different thing as you back up to t = 11 from the right. Since there is no ONE number that the value "ought" to be (regardless of direction of approach), then there is no actual limit value.