`lim_(n-gt0)(sin2n)/(2n^2+n)`

lim_(n->oo)sin(x/2^n)/(x/2^n)

lim_(n->oo)(sin((a)/(2^n)))/(sin((b)/(2^(n+1))))=

lim_(nto0)(1/n^(2)+2/n^(2)+3/n^(2)+...+n/n^(2)) is

Prove that, lim_(ntooo)[(n)/(n^(2))+(n+1)/(n^(2))+(n+2)/(n^(2))+.......+(2n)/(n^(2))]=(3)/(2)

Evalute : lim_(ntooo)[(n)/(n^2+1^2)+(n)/(n^2+2^2)+........+(1)/(2n)] .

lim_(ntooo)[(n)/(n^(2)+1)+(n)/(2^(2)+n^(2))+.........+(1)/(2n)]

lim_(n->oo)2^(n-1)sin(a/2^n)

(2) lim_(n rarr0) (n!sin x)/(n)

lim_ (n rarr0) (sin ^ (2) n) / (n ^ (2))

If f(n)=lim_(xto0) {(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"sin"(x)/(2^(n)))}^((1)/(x)) then find lim_(ntooo) f(n).