1.

`lim_(n to oo) x^(2)sin(log_(e)sqrt(cos((pi)/(x))))` is less thenA. `0`B. `-(pi^(2))/(2)`C. `-(pi^(2))/(4)`D. `(pi^(2))/(8)`

Answer» Correct Answer - 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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