What is the value of the following?
$$\lim_{x \to \infty} e^{-ix}$$
I have looked at a few criteria for convergence, such as the simple ratio test, or the integral test.
In this case the expression $e^{ix}$ rotates around a unit circle as $x$ grows.
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It doesn't exist. – Chappers Jun 13 '18 at 22:03
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3Is $x$ real, imaginary, or complex? – Cameron L. Williams Jun 13 '18 at 22:03
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1The tests you mention pertain to infinite sums...it isn't clear how you intend to apply them to this problem. – lulu Jun 13 '18 at 22:04
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@TariqRashid Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here https://meta.stackexchange.com/questions/5234/how-does-accepting-an-answer-work – user Aug 04 '18 at 22:07
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Yes it "rotates clockwise around a unit circle" as $x$ grows and therefore the limit doesn't exist.
Arnaud Mortier
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(+1) Sorry about the edit, I edited consistently with the title, which is inconsistent with the main body. – Arnaud Mortier Jun 13 '18 at 22:28
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