InterviewSolution
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InterviewSolution
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If `|cos^-1(1)/(n)|lt (pi)/(2)`, then `lim_(n to oo) {(n+1)(2)/(pi)cos^-1.(1)/(n)-n}`A. `(2-pi)/(pi)`B. `(pi-2)/(pi)`C. `1`D. `0` |
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Answer» Correct Answer - B `lim_(n to oo) {(n+1)(2)/(pi)cos^-1.(1)/(n)-n}` `=lim_(n to oo) (2)/(pi){(n+1)cos^-1.(1)/(n)-(pi)/(2)n}` `=lim_(n to oo) (2)/(pi){n(cos^-1.(1)/(n)-(pi)/(2))+cos^-1.(1)/(n)}` `=lim_(n to oo) (2)/(pi){nsin^-1.(1)/(n)-(pi)/(2)+cos^-1.(1)/(n)}` `=lim_(n to oo) (2)/(pi){(sin^-1.(1)/(n))/((1)/(n))+cos^-1.(1)/(n)}=(2)/(pi)(-1+(pi)/(2))=(pi-2)/(pi)` |
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