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

[Poirot]

Homework Statement

The function is f_A(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 f_A(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!

 

[mfb]

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.

 

[Poirot]

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 :)!