`lim_(n->oo)(n^(alpha)sin^2n !)/(n+1), 0ltalphalt1`, is equal to :

lim_(n to oo) (n^(p) sin^(2)(n!))/(n +1) , 0 lt p lt 1 , is equal to-

lim_(xrarr oo) (n^p sin^2(n!))/(n+1),0ltplt1 , is equal to

lim_(xrarr oo) (n^p sin^2(n!))/(n+1),0ltplt1 , is equal to

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

("lim")_(n vec oo)"{"(n/(n+1))^(alpha)+sin (1/n)]^n (when alpha in Q ) is equal to (a) e^(-alpha) (b) -alpha (c) e^(1-alpha) (d) e^(1+alpha)

lim_(ntooo) {((n)/(n+1))^(alpha)+"sin"(1)/(n)}^(n) (where alphainQ ) is equal to

lim_(ntooo) {((n)/(n+1))^(alpha)+"sin"(1)/(n)}^(n) (where alphainQ ) is equal to

If 0 lt alpha lt beta then lim_(n to oo) (beta^(n) + alpha^(n))^((1)/(n)) is equal to

If 0 lt alpha lt beta then lim_(n to oo) (beta^(n) + alpha^(n))^((1)/(n)) is equal to