`lim_(n->oo) (sqrt(n+1)-sqrtn)=0`

Evaluate the following limit: (lim)_(n->oo)(sqrt(x+1)-sqrt(x))sqrt(x+2)

The value of lim_(n->oo)(sqrt(1)+sqrt(2)+sqrt(3)+.....+sqrt(n))/(nsqrt(n)) is

lim_(n->oo) nsin(1/n)

lim_(n rarr oo)n[sqrt(n+1)-sqrt(n))]

lim_(n to oo)[(sqrt(n+1)+sqrt(n+2)+....+sqrt(2n))/(n sqrt((n)))]

lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

The value of : lim_(ntooo)((1)/(sqrtn sqrt(n+1))+(1)/(sqrtn sqrt(n+2))+ (1)/(sqrtn sqrt(n +3)) + ...... +(1)/(sqrtn sqrt(2n))) is:

The value of lim_(nto oo)(sqrt(n^(2)+n+1)-[sqrt(n^(2)+n+1)]) where [.] denotes the greatest integer function is

lim_(n->oo)[1/sqrt(2n-1^2) +1/sqrt(4n-2^2)+1/sqrt(6n-3^2)+...+1/n]

lim_(n rarr oo)(3+sqrt(n))/(sqrt(n))