Left-&Right-Handed Limits Explained: What Do 150 & 300 mg Mean?

In summary, the left- and right-handed limits for the function f(t) are 150 mg and 300 mg, respectively. These values may represent measurements taken at t = 12 hours, with the left-hand limit being taken just before t = 12 and the right-hand limit being taken just after t = 12. It is unclear why f(0) is not equal to 150 mg, but it is possible that this measurement was taken at a different time point.
  • #1
bigplanet401
104
0
img.jpg

Homework Statement



See attached image.

Homework Equations



Left- and right-handed limits.

The Attempt at a Solution



I know lt (t -> 12-) f = 150 mg and lt (t -> 12+) f = 300 mg, but I don't know how to explain these numbers. I'm assuming that measurements are taken and that this graph is from these measurements. But then why can't we say f(0) = 150 mg? Does this mean that a measurement is taken "a short time after" the drug is given? Thanks for any help.
 
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  • #2
bigplanet401 said:

Homework Statement



See attached image.

Homework Equations



Left- and right-handed limits.

The Attempt at a Solution



I know lt (t -> 12-) f = 150 mg and lt (t -> 12+) f = 300 mg, but I don't know how to explain these numbers. I'm assuming that measurements are taken and that this graph is from these measurements. But then why can't we say f(0) = 150 mg?
Don't you mean f(12)?
bigplanet401 said:
Does this mean that a measurement is taken "a short time after" the drug is given? Thanks for any help.
It seems that a measurement is made right at t = 12.
 
  • #3
Forgot to post image...sorry. Please see top post.
 
  • #4
Now that I can see the image, it looks like measurements are made just after 4, 8, 12, and 16 hours.
 

Related to Left-&Right-Handed Limits Explained: What Do 150 & 300 mg Mean?

1. What is the difference between left-handed and right-handed limits?

Left-handed and right-handed limits refer to the direction from which a function is being approached at a specific point. A left-handed limit is when the function is being approached from the left side of the point, while a right-handed limit is when the function is being approached from the right side of the point.

2. How are left-handed and right-handed limits calculated?

Left-handed and right-handed limits are calculated by evaluating the function at points that are getting closer and closer to the point of interest from either the left or right side. This can be done by using a table, graph, or algebraic manipulation.

3. What does 150 mg mean in the context of left-handed and right-handed limits?

In the context of left-handed and right-handed limits, 150 mg refers to the value of the limit as the function approaches a specific point from the left side. It is the value that the function is approaching as the input approaches the point from the left side.

4. What does 300 mg mean in the context of left-handed and right-handed limits?

In the context of left-handed and right-handed limits, 300 mg refers to the value of the limit as the function approaches a specific point from the right side. It is the value that the function is approaching as the input approaches the point from the right side.

5. Why are left-handed and right-handed limits important?

Left-handed and right-handed limits are important because they help us understand the behavior of a function at a specific point. They can also be used to determine if a function is continuous at that point, and can be used in more advanced mathematical concepts such as derivatives and integrals.

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