`lim_n->0 ((p^(1/n) +q^(1/n))/2)^n, p,q gt0` equals

lim_(n rarr0){(p^((1)/(n))+q^((1)/(n)))/(2)}^(n),p,q>0

lim_(nto oo) ((nsqrt(p)+nsqrt(q))/(2))^n,p,q,gt 0 equals

Evaluate the following limits: lim_(x to oo)(q^(n)+p^(n))^(1//n), 0 lt p lt q

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

Let a_(1)gta_(2)gta_(3)gt...gta_(n)gt1. p_(1)gtp_(2)gtp_(3)gt...gtp_(n)gt0" such that "p_(1)+p_(2)+p_(3)+...+p_(n)=1. Also, F(x)=(p_(1)a_(1)^(x)+p_(n)a_(n)^(x))^(1//x) . lim_(xto0^(+)) F(x)" equals "

Let a_(1)gta_(2)gta_(3)gt...gta_(n)gt1. p_(1)gtp_(2)gtp_(3)gt...gtp_(n)gt0" such that "p_(1)+p_(2)+p_(3)+...+p_(n)=1. Also, F(x)=(p_(1)a_(1)^(x)+p_(n)a_(n)^(x))^(1//x) . lim_(xto0^(+)) F(x)" equals "

If lim_(x rarr 0) (1 + px)^(q/x) = e^(4), where p,q in N , then

If lim_(x rarr 0) (1+px)^(q//x) = e^(4) , where p, q, in N, then :