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no
sin x / x is equal to one only when x tends to zero. In your case x is equal to 8 which is not zero so it is not equal to one.
Hello alexie !
Well let me explain some concepts of limit in this case ..!
Lim x--> a sin(x)/(x) = b
Now b can be any number depending on the variation in the 'a' ...
The most beautiful case of this type is ...! when a tends to zero !
i.e when Lim x-->0 sin(x)/(x) = b
then b === 1
sin(8)/(8) is not equal to 1 because x-->8
sin(pi/2)/pi/2 is not equal to 1 ...because x-->pi/2
-------------
Sin(x-3)/(x-3) becomes one ...when x-->3 ( because it also comes in the same form ..sin(0)/(0) )
So Lim x-->3 sin(x-3)/(x-3) = Lim x-->0.5 sin(x-0.5)/(x-0.5) = Lim x-->0 sin(x)/(x) = 1
Hope it is clear now
With regards
Yagya
askiitians_expert
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