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

Lt_(x to oo)((1^(1//x)+2^(1//x)+3^(1//x)+...+n^(1//x))/(n))^(nx)=

lim_(x->oo)(1-x+x.e^(1/n))^n

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

If lim_(x rarr(oo) (1+(1)/(x(x+2)))^(x^(2))(1+(1)/(x(x+4)))^(-x^(2)) is equal to e^(n) then n is equal to

lim_(x->oo)(e^x((2^(x^n))^(1/(e^(x)))-(3^(x^n))^(1/(e^(x)))))/(x^n), n in N, is equal to

(lim_(xto oo) ((x+3)/(x+1))^(x+1) is equal to

lim_(x->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x (c) (log)_e x (d) none of these

Evaluate the following limits: lim_(x to oo) ((1^(x)+2^(x)+....+n^(x))/(n))^(n//x)

Let f : R to R be a real function. The function f is double differentiable. If there exists ninN and p in R such that lim_(x to oo)x^(n)f(x)=p and there exists lim_(x to oo)x^(n+1)f(x) , then lim_(x to oo)x^(n+1)f'(x) is equal to