Evaluate `underset(ntooo)limnsin(2pisqrt(1+n^(2))),(n inN).`

Evaluate underset(ntooo)limcos(pisqrt(n^(2)+n)) when n is an integer.

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

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

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

Evaluate underset(ntooo)limn^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))...(n+2^(-n+1))]^(n) .

Find the value of underset(ntooo)lim[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(ntooo)(n-sqrt(n^(2)+n))

Evaluate lim_(ntooo) (-1)^(n-1)sin(pisqrt(n^(2)+0.5n+1)),"where "nin N

Evaluate lim_(ntooo) (-1)^(n-1)sin(pisqrt(n^(2)+0.5n+1)),"where "nin N

Evaluate lim_(ntooo) cos(pisqrt(n^(2)+n)) when n is an integer.