InterviewSolution
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InterviewSolution
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Let `f(x)=lim_(n to oo) ((2 sin x)^(2n))/(3^(n)-(2 cos x)^(2n)), n in Z`. ThenA. at `x=n pm(pi)/(6)`, f(x) is discontinuousB. `f((pi)/(3))=1`C. f(0)=0D. all of the above |
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Answer» Correct Answer - D We have `,f(x)=underset(n to oo)lim ((sin^(2)x)^(n))/(((3)/(4))^(n)-(cos^(2)x)^(n))` In the neighbourhood of `x=n pi pm (pi)/(6)`, we have `f(x)=(0)/(0-0)`, which does not exist. Hence, f(x) is discontinuous at `x=n pi pm pi//6, n in Z` Also, we have `f((pi)/(3))=underset(n to oo)lim ((3)/(3))^(n)/(((3)/(4))^(n)-((1)/(4))^(n))=underset(n to oo)lim (1)/(1-((1)/(3))^(n))=1` `and f(0)=underset( n to oo)lim (0)/(((3)/(4))^(n)-1)=0` Hence, option (a),(b) and (c ) are correct. |
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