Evaluate `lim_(ntooo) nsin(2pisqrt(1+n^(2))),(n inN).`

1.	Evaluate `lim_(ntooo) nsin(2pisqrt(1+n^(2))),(n inN).`
Answer» L= `underset(ntooo)limnsin(2pisqrt(1+n^(2)))` `underset(ntooo)limnsin(2pisqrt(1+n^(2))-2npi)` `underset(ntooo)limnsin{(2pi(sqrt(1+n^(2))-n))/((sqrt(1+n^(2))+n))(sqrt(1+n^(2))+n)}` `=underset(ntooo)lim{(nsin((2pi)/(sqrt(1+n^(2))+n)))/(((2npi)/(sqrt(1+n^(2))+n)))((2pi)/(sqrt(1+n^(2))+n))}` `underset(ntooo)lim(2npi)/(n(sqrt(1+(1)/(n^(2)))+1))` `=(2pi)/(2)=pi`

Discussion

`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)`
If `lim_(xto oo){(x^2+1)/(x+1)-(ax+b)}to oo`, thenA. `a in (1,oo)`B. `a ne 1 , b in R`C. `a in (-oo,1)`D. none of these
Evaluate:\(\lim\limits_{x \to 1}\frac{\sqrt {1+x}-\sqrt {1-x}}{1+x}\)
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`lim_(xrarr0) ((1-cos2x)^2)/(2xtanx-xtan2x)` , isA. 2B. `-(1)/(2)`C. `(1)/(2)`D. `-2`
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