Evaluate: ` lim_(x->oo) { ((a_1)^(1/x)+(a_2)^(1/x)+.... +(a_n)^(1/x))/n}^(nx)`

Evaluate: ("lim")_(xvecoo)((a_1^( 1/x)+a_2^ (1/x)+ --+a_ n^(1/x))/n)^(n x)

Evaluate: ("lim")_(xvecoo)((a_1^( 1/x)+a_2^ (1/x)+ --+a_ n^(1/x))/n)^(n x)

lim_(x->oo)((1^(1/x) +2^(1/x) +3^(1/x) +...+n^(1/x))/n)^(nx) is equal to

lim_(x rarr oo){((a_(1))^((1)/(x))+(a_(2))^((1)/(x))+...+(a_(n))^((1)/(x)))/(n)}^(nx)

Evaluate: ("lim")_(nvecoo)((a1 1/x+a2 1/x++a n1/x)/n)^(n x)

lim_ (x rarr oo) ((1 ^ ((1) / (x)) + 2 ^ ((1) / (x)) + 3 ^ ((1) / (x)) ++ n ^ ((1 ) / (x))) / (n)) ^ (nx), n in N

lim_ (x rarr oo x rarr oo) ((1 ^ ((1) / (x)) + 2 ^ ((1) / (x)) + 3 ^ ((1) / (x)) + ... + n ^ ((1) / (x))) / (n)) ^ (nx) is

The value of lim_(x rarr oo)(x^(n)+nx^(n-1)+1)/(e^(|x|)),n in1 is

{a_n} and {b_n} are two sequences given by a_n=(x)^(1//2^n) +(y)^(1//2^n) and b_(n)=(x)^(1//2^n)-(y)^(1//2^n) for all n in N. The value of a_1 a_2 a_3……..a_n is equal to