# Find the Limits: Testing the Boundaries

• PistonsMVP
In summary, we discussed finding limits and how they are used to determine the behavior of a function at a specific point. We also clarified that a limit is not complaining, but rather stating a fact that the function is not defined at that point. For the first example, the limit is 312 as x approaches 11+. For the second example, the limit is undefined, as shown by the fact that the value approaches different values when approaching from the left and right side of x=1.
PistonsMVP
Find the Limits1. lim 312
x->11+

2. lim (x^2 +9)/(x^2 -1)
x->1for #2 i got 10 as the answer, but I'm not sure if its right. Thanks

edit: Sorry, wrong forum

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1) do you know what a limit is? if so, looking at the behavior of the function should hint you as to what the answer is.

2) 10 isn't the correct answer. many people confuse the answers of 0/0 and x/0 or 0/x. The former gives odd results, whereas the latter two produce the same result, no matter what x is.

phreak what do you mean by "the former gives odd results?"PistonsMVP, the limit of a contant function is what?

nm i figured it out. #1 is 312
and #2 DNE because 10/0

excuse me...isnt the point of a limit to find what value it approaches and not complain that its undefined?

btw the 2nd limit is -infinity

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Gib Z said:
excuse me...isnt the point of a limit to find what value it approaches and not complain that its undefined?

o btw the 2nd limit is -5

How is it -5?

d_leet said:
How is it -5?

It is not -5. And there is a big difference between 10/0, which is undefined, and the limit of the function as x -> 1.

Gib Z said:
excuse me...isnt the point of a limit to find what value it approaches and not complain that its undefined?

btw the 2nd limit is -infinity
Saying that the limit is -infinity is just a way of saying that it is not defined. Saying that a limit is undefine is not "complaining", it is stating a fact.

$$\lim_{x \to a} f(x) = +\infty$$ or $$\lim_{x \to a} f(x) = -\infty$$

Just describes HOW a limit is not defined (whether it can be made arbitrarily large positive/large negative as x->a), but it definitely is not defined!

## 1. What is the purpose of "Find the Limits: Testing the Boundaries"?

The purpose of "Find the Limits: Testing the Boundaries" is to investigate the boundaries and limitations of a particular system, concept, or phenomenon. This can help scientists better understand the capabilities and constraints of various systems and potentially push the boundaries of what is known and possible.

## 2. How do scientists determine the limits of a system?

Scientists use a variety of methods to determine the limits of a system. This may include conducting experiments, making observations, and analyzing data to identify patterns and trends. They may also use mathematical models and simulations to test the boundaries of a system and make predictions about its behavior.

## 3. What are some potential benefits of testing the boundaries of a system?

Testing the boundaries of a system can lead to a better understanding of its capabilities and limitations. This can help scientists develop more accurate models and predictions, improve technologies and processes, and discover new possibilities and solutions.

## 4. What are some potential risks of pushing the limits of a system?

Pushing the limits of a system can also have potential risks. Depending on the system being tested, there may be safety concerns or unintended consequences. It is important for scientists to carefully consider the potential risks and take necessary precautions when conducting experiments or pushing the boundaries of a system.

## 5. How can the results of testing the boundaries of a system be applied?

The results of testing the boundaries of a system can be applied in various ways. For example, they can inform the development of new technologies, help improve existing systems, and contribute to our overall understanding of the natural world. The findings may also have practical applications in fields such as engineering, medicine, and environmental science.

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