Going senile at 30

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ZaidAlyafey

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Yesterday I posted a question on Stack Exchange that was so trivial that I think I might be going senile at the age of 30. That, or I was under the influence of something.

Does $\lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0$?
Yeah, I must confess , that wasn't easy to see at the first glance, at least for me. I was trying just like you to find an upper bound

ZaidAlyafey

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MHB Math Helper
Well, I guess I am going senile at the age of 23

Random Variable

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And then mrf had to rub it in by mentioning that $e^{iz}$ of course has an elementary antiderivative that is valid everywhere since $e^{iz}$ is an entire function.

I could have at least recognized that there was no justification for bringing the limit inside of the integral due to the fact that parametrization of the integral brings an $R$ out front.

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ZaidAlyafey

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MHB Math Helper
Actually, it isn't always easy to see that a function along a contour approaches zero for large or small quantities of the modulus. It is always the hard part when using complex analysis approaches.

I recognized that the function has an anti-derivative but that was a little bit late .

Deveno

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MHB Math Scholar
I went senile already. Wasn't working for me.

chisigma

Well-known member
Yesterday I posted a question on Stack Exchange that was so trivial that I think I might be going senile at the age of 30. That, or I was under the influence of something.

Does $\lim_{R \to \infty} \int_{C_{R}} e^{iz} \ dz \to 0$?
If You allow an 'oversixty' to do You a suggestion, then the suggestion is...

... sometime just take it easy! ...

Kind regards

$\chi$ $\sigma$

mathbalarka

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MHB Math Helper
I am already senile at 13. I once thought about a long time why there is no prime $\geq 3$ of the form $x^3+y^3$.

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mathbalarka

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Ah, but I will refer myself as 13 ever afterwards until 17, as 14 is not of my likes, neither is 15 or 16!

MarkFL

Staff member
Ah, but I will refer myself as 13 ever afterwards until 17, as 14 is not of my likes, neither is 15 or 16!
I guess if Jack Benny could be 39 forever, then you can be 13 for a few years.

Jameson

Staff member
I'm in my mid twenties and often feel I'm just not as sharp as I used to be. Doesn't bode well for my 30's and 40's.

ZaidAlyafey

Well-known member
MHB Math Helper
If You allow an 'oversixty' to do You a suggestion, then the suggestion is...

... sometime just take it easy! ...

Kind regards

$\chi$ $\sigma$
True. Working with some complicated stuff , you always miss the trivial. Sometimes it needs no more than thinking simple to find the solution.

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ModusPonens

Well-known member
Is there a converse of Morera's theorem?