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Mainak Chakraborty Grade: Upto college level
`        The value of limx →0 ( sin x / x)sinx /x -sinx is : `
7 years ago

19 Points
```										Dear Mainak,
Substituting the value x=0 in the limit we get this limit of the form
18 .Thus this is the indeterminate form of the limit.
We can write it as
lim x-->0 (1+(sin x - x)/x)^[sin x/(x-sin x)]
Making the use of the  property
lim x-->0 (1+f(x))^(1/f(x))=e,when lim x-->0 f(x) =0
Therefore Rewriting above as
lim x-->0 (1+(sin x - x)/x)^[sin x/(x-sin x)][x/sin x]
or lim x-->0 (1+(sin x - x)/x)^[x/(sin x- x)][sin x/x](-1)
=     e^ lim x-->0 (sin x/x)(-1)
=e^(1)(-1)
=1/e
Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.
All the best  MAINAK!!!

Regards,
MOHIT
```
7 years ago
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