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/sci/ - Science & Math

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6156972 No.6156972 [Reply] [Original]

Does the limit as t tends to 0 of e^-it exist?

I think the limit is 1 but the prof said it doesn't exist and there was no time to ask him to explain.

pls explain

>> No.6156980

e^ix = cos(x) + isin(x) now think.

>> No.6156984
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6156984

Here's what wolfram has to say

>> No.6156993

your prof is a fag because the limit is 1 indeed

>> No.6157002

>>6156993
>>6156984
Fuck, I need to speak to this nigger on Monday then.

>> No.6157012
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6157012

Something is seriously wrong with your prof.

>> No.6157581

>>6156972

If t is real, yes. If t is complex, no.

>> No.6157621
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6157621

>>6157581
>implying exponential is discontinuous

>> No.6157628

look at it in terms of rotations in the complex plane. Shit is trivial.

>> No.6157629

>>6157581
e^(-it) is continuous in all complex plane (moreover, it's analytic everywhere). So, no, for any t limit e^(-it) as t goes to 0 is equal to e^(i*0)=1

>> No.6158151

>>6157629

Oops I accidentally retarded. It's because I'm an engineer...I can't help it.