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do you agree that the limit of sin 8/8 is equal to 1?

do you agree that the limit of sin 8/8 is equal to 1?

Grade:

3 Answers

KARAN ACHARYA
52 Points
9 years ago

no

Harsh Jhawar
19 Points
9 years ago

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.

Askiitians_Expert Yagyadutt
askIITians Faculty 74 Points
9 years ago

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

 

All have same meaning and same limit value .. !

Hope it is clear now

 

With regards

 

Yagya

askiitians_expert

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