In the limit as A --> ∞, what does the function become?

In summary, the conversation discusses the function fA(x) and the Dirac delta function. It is suggested that the answer to the problem is 2 times the delta distribution, and it is noted that x should not be used as both a variable and a multiplication sign. The speaker apologizes for using the term "function" instead of "measure" and for using x as a multiplication sign.
  • #1
Poirot
94
3

Homework Statement


The function is fA(x) = A, |x| < 1/A, and 0, |x| > 1/A

Homework Equations


δ(x) = ∞, x=1, and 0 otherwise

The Attempt at a Solution


I think the answer is the Dirac delta function, however I noticed that if you integrate fA(x) between -∞ and ∞ you get 2, which if I remember rightly to be a Dirac delta function this should be 1? So perhaps the answer is 2 x δ(x)?
I'm not sure what's correct, so any help would be greatly appreciated, thank you!
 
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  • #2
2 times the delta distribution (it is not a function), correct.
Avoid using x as variable and multiplication sign at the same time, please. * is the typical multiplication sign in ascii.
 
  • #3
mfb said:
2 times the delta distribution (it is not a function), correct.
Avoid using x as variable and multiplication sign at the same time, please. * is the typical multiplication sign in ascii.
Great thank you, and apologies, I'm aware it's not a function but a measure, but alas my lecturer uses the term function and so it's stuck with me. As for x for multiply, laziness is all, sorry... thanks again, much appreciated :)!
 

FAQ: In the limit as A --> ∞, what does the function become?

What does "A --> ∞" mean in this context?

In mathematics, the notation "A --> ∞" means that the value of A is approaching infinity, or becoming infinitely large.

Why is the limit as A approaches infinity important?

The limit as A approaches infinity is important because it allows us to understand the behavior of a function as the input (A) becomes increasingly large. This can provide valuable insights into the overall behavior and trends of the function.

How do you calculate the limit as A approaches infinity?

To calculate the limit as A approaches infinity, you can use a variety of methods such as algebraic manipulation, factoring, or using L'Hôpital's rule. It is important to first simplify the function as much as possible before evaluating the limit.

Can the limit as A approaches infinity be a finite number?

Yes, the limit as A approaches infinity can be a finite number. This would occur if the function approaches a specific value or constant as A becomes infinitely large.

What are some real-world applications of the limit as A approaches infinity?

The concept of limits, particularly as A approaches infinity, is used extensively in physics, engineering, and economics to model and analyze various systems. For example, in physics, the limit as time approaches infinity can be used to predict the behavior of a system in the long run.

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