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Question: Limit inferior and Limit Superior Output for limit

Question:Limit inferior and Limit Superior Output for limit

Adam Ledger 360 Maple
plot range limit
February 16 2018
0


 

> 

limit(Re(exp(1/4-(1/4)*signum(x))*cos((1/2)*ln(abs(x))/Pi)-I*exp(1/4-(1/4)*signum(x))*sin((1/2)*ln(abs(x))/Pi)), x = infinity)

-1 .. 1

 (1)
> 

limit(Re(exp(1/4-(1/4)*signum(x))*cos((1/2)*ln(abs(x))/Pi)-I*exp(1/4-(1/4)*signum(x))*sin((1/2)*ln(abs(x))/Pi)), x = -infinity)

-exp(1/2) .. exp(1/2)

 (2)
> 

``


 

Download maplehelp_limit_inferior_superior.mw

Hello, i was just curious about why when i plot the function it indicates the values for both the limits are actually the limit sups, and if anyone has a good reference for me as far as computing these limits by hand and verifying that the precise limit does not actually exist, but can only be indicated by the range (inf(L),sup(L)) as the output suggests.

 

Thankyou in advance!
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