`lim_(n->oo){(n/(n+1))^alpha+sin(1/n)}^n` where `alpha epsilon Q` is equal to:

("lim")_(nvecoo)"{"(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

("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_(x rarr){((n)/(n+1))^(alpha)+s in(1)/(n)]^(n) (when alpha in Q ) is equal to (a) e^(-alpha)(b)-alpha(c)e^(1-alpha)(d)e^(1+alpha)

lim_(n to oo)(n!)/((n+1)!-n!)

lim_ (n rarr oo) (n ^ (alpha) sin ^ (2) n!) / (n + 1), 0

lim_ (n rarr oo) {((n) / (n + 1)) ^ (alpha) + sin ((1) / (n))} ^ (n) where

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