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Have I calculated the limit correctly?

May 22, 2023, 4:57 am
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0
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.

Download limit_int.mw

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