The value of `lim_(n->oo)[(2n)/(2n^2-1)cos((n+1)/(2n-1))-n/(1-2n)dot(n(-1)^n)/(n^2+1)]i s` (a) 1 (b) `-1` (c) 0 (d) none of these

Options

A. 5
B. 6
C. 7
D. none of these

Answer

C

Explanation

`underset(ntooo)lim[(2)/(2-(1)/(n^(2))).(1)/(n)cos((1+1//n)/(2-1//n))-(1)/(((1)/(n)-2)).(1)/((1+(1)/(n^(2)))).(1)/(n)]`
`=underset(ntooo)lim(1)/(n)[(2)/(2-(1)/(n^(2))).cos((1+(1)/(n))/(2-(1)/(n)))-(1)/(((1)/(n)-2)).(1)/((1+(1)/(n^(2))))]`
`=0xx[(2)/(2)xx"cos"(1)/(2)+(1)/(2)xx(1)/(1)]=0`.