`("lim")_(xvecoo)"{"(n/(n+1))^(alpha)+s in1/n]^n`(when `alpha in Q`) is equal to (a) `e^(-alpha)` (b) `-alpha` (c) `e^(1-alpha)` (d) `e^(1+alpha)`

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

cos (n + 1) alpha cos (n-1) alpha + sin (n + 1) alpha sin (n-1) alpha =

cos(n+1) alpha * cos(n-1)alpha + sin (n+1)alpha * sin (n-1) alpha =

( sin(n+1) alpha - sin (n-1)alpha )/( cos (n+1) alpha + 2 cos n alpha + cos (n-1) alpha )=

If alpha=e^((i2 pi)/(n)), then n(11-alpha)(11-alpha^(2))(11-alpha^(n-1))=

If alpha is the nth root of unity,then 1+2 alpha+3 alpha^(2)+rarr n terms equal to a.(-n)/((1-alpha)^(2)) b.(-n)/(1-alpha^(2)) c.(-2n)/(1-alpha) d.(-2n)/((1-alpha)^(2))

If alpha is the nth root of unity, then 1+2alpha+3alpha^2+ ton terms equal to a. (-n)/((1-alpha)^2) b. (-n)/(1-alpha) c. (-2n)/(1-alpha)"" d. (-2n)/((1-alpha)^2)