lim x tends to pi,sin3x-3sinx/(pi-x)^3

Dear student
We have,limxπsin3x-3sinxπ-x3=limxπ3sinx-4sin3x-3sinxπ-x3=-4limxπsin3xπ-x3=-4limxπsin3π-xπ-x3=-4limxπsinπ-xπ-x3=-4×13=-4
Regards

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Hello Prithvi dear, as we apply pi to x we get 0/0. So indeterminate form
In this situation L' hopithal rule is to be applied
It is just differentiating nr and dr separately
So it gets changed into after differentiation as (3 cos 3x  - 3 cos x) / 3(pi - x)^2 (-1)
This is changed as (cos x - cos3x) / (pi - x)^2
Now 0/0 indeterminate
Again rule, (- sin x + 3 sin 3x) / 2 (pi -x) (-1)
So changed as 1/2 * ( sin x - 3 sin 3x) / (pi - x)
Once again rule, 
1/2 * (9 cos 3x - cos x) 
Now applying limit 1/2 * 8 = 4
 
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