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

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

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

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

p=sum_(n=0)^(oo) (x^(3n))/((3n)!) , q=sum_(n=1)^(oo) (x^(3n-2))/((3n-2)!), r = sum_(n=1)^(oo) (x^(3n-1))/((3n-1)!) then p + q + r =

If 0ltpltq then lim_ (n rarr oo)(q^(n)+p^(n))^(1/n)=

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