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Question: Have I calculated the limit correctly?

Question:Have I calculated the limit correctly?

EugeneKalentev 85 Maple
calculus integral limit
May 22 2023
0

I calculate the limit

Let me know if there are any errors in my calculations?


 

> 

restart
> 

assume(a > 0)
> 

limit(int(sin(x)/x, x = n .. n+a), n = infinity)

0

 (1)
> 

int(sin(x)/x, x = n .. n+a)

-Si(n)+Si(n+a)

 (2)
> 

plot3d(-Si(n)+Si(n+a), a = -5 .. 5, n = -5 .. 5)

 
> 

limit(-Si(n)+Si(n+a), n = infinity)

0

 (3)
> 

limit(-Si(n), n = infinity)

-(1/2)*Pi

 (4)
> 

limit(Si(n+a), n = infinity)

(1/2)*Pi

 (5)
> 

NULL


Thank you in advance.

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