The value of `lim_(nrarroo) ((sqrtn^(2)+n-1)/(n))^(2sqrt(n^(2)+n-1))` isA. eB. `1//e`C. `e^(2)`D. `e^(-2)`

The value of `lim_(nrarroo) ((sqrtn^(2)+n-1)/(n))^(2sqrt(n^(2)+n-1))`

1.	The value of `lim_(nrarroo) ((sqrtn^(2)+n-1)/(n))^(2sqrt(n^(2)+n-1))` isA. eB. `1//e`C. `e^(2)`D. `e^(-2)`
Answer» Correct Answer - B `L=underset(nrarroo)(lim)((sqrt(n^(2)+n)-1)/(n))^(2sqrt(n^(2)+n)-1)` `=e^(underset(nrarroo)(lim)[(sqrt(n^(2)+n)-1-n)/(n)](2sqrt(n^(2)+n)-1))` `=e^(underset(nrarroo)(lim)([(n^(2)+n)-(1+n)^(2)](2sqrt(n^(2)+n)-1))/(n{sqrt(n^(2)+n)+(1+n)}))` `=e^(underset(nrarroo)(lim)((-n-1)(2sqrt(n^(2)+n)-1))/(n{sqrt(n^(2)+n)+(1+n)}))` `=e^(underset(nrarroo)(lim)((-1-(1)/(n))(2sqrt(1+(1)/(n))-(1)/(n))n^(2))/(n^(2){sqrt(1+(1)/(n))+(1)/(n)+1})=e^(-1))`

`lim_(xto oo) (1)/(n) {1+e^(1//n)+e^(2//n)+e^(3//n)+.....+e^((n-1)/(n))}` is equal toA. eB. `-e`C. `e-1`D. `1-e`
`lim_(xto oo) ((nsqrt(a)+nsqrt(b))/(2))^n,a,b,gt 0` equalsA. 1B. `sqrt(pq)`C. `pq`D. `(pq)/(2)`
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