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# Computing the limit of a distribution watch

1. Let be the distribution . I want to determine the .

I thought about using L'Hospital's rule, since

And

However, since for we have , we can see that the limit

will not be well defined. Does anyone have a better suggestion? Note that obviously .
2. Okay, I had another attempt. So, we have

Recall that

Then

and

Hence

Thus

and so we can conclude that
3. (Original post by RamocitoMorales)
Let be the distribution . I want to determine the .

I thought about using L'Hospital's rule, since

I think this is the more successful approach. Can't you write the above in terms of the derivative of the test function?
4. (Original post by RichE)
I think this is the more successful approach. Can't you write the above in terms of the derivative of the test function?
See the edit in the post above. I achieve a distributional result via the other approach.
5. (Original post by RamocitoMorales)
See the edit in the post above. I achieve a distributional result via the other approach.
Correct - but you could have got that much more quickly (in a line or two) from where I cut off the edit of your first approach.

PS you may have a minus sign missing in your answer.
6. (Original post by RichE)
Correct - but you could have got that much more quickly (in a line or two) from where I cut off the edit of your first approach.
I agree that my method is far too long and complicated. Can you expand on what you mean by writing the derivatives of the test function?
7. (Original post by RamocitoMorales)
I agree that my method is far too long and complicated. Can you expand on what you mean by writing the derivatives of the test function?

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