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lim(n to oo) x^(2)sin(log(e)sqrt(cos((pi...

`lim_(n to oo) x^(2)sin(log_(e)sqrt(cos((pi)/(x))))` is less then

A

`0`

B

`-(pi^(2))/(2)`

C

`-(pi^(2))/(4)`

D

`(pi^(2))/(8)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`underset(xtoinfty)lim(x^(2)sin(log_(e)sqrt(cos((pi)/(x)))))/(log_(e)sqrt(cos((pi)/(x)))).log_(e)sqrt(cos((pi)/(2x)))`
`=underset(xtoinfty)lim(x^(2))/(2)(log_(e)[1+(cos((pi)/(x))-1)])/((cos((pi)/(x))-1))(-sin^(2)((pi)/(2x)))`
`=-(pi^(2))/(4)`
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