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

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)

If [x] denotes the greatest integer less than or equal to x , then evaluate ("lim")_(nvecoo)1/(n^3){[1^2x]+[2^2x]+[3^2x]+}[n^2x]}

If L=("lim")_(nvecoo)(2x3^2x2^3x3^4 x2^(n-1)x3^n)^1/((n^(2+1)) , then the value of L^4 is

If f(x) is integrable over [1,], then int_1^2f(x)dx is equal to ("lim")_(nvecoo)1/nsum_(r=1)^nf(r/n) ("lim")_(nvecoo)1/nsum_(r=n+1)^(2n)f(r/n) ("lim")_(nvecoo)1/nsum_(r=1)^nf((r+n)/n) ("lim")_(nvecoo)1/nsum_(r=1)^(2n)f(r/n)

If L=("lim")_(nvecoo)(2x3^2x2^3x3^4..... x2^(n-1)x3^n)^(1/((n^(2+1))) , then the value of L^4 is

Discuss the continuity of f(x)=(lim)_(nvecoo)(x^(2n)-1)/(x^(2n)+1)

If ("lim")_(nvecoo)1/((sin^(-1)x)^("n")+1)=1,t h e n find the value of x

If a_1=1a n da_(n+1)=(4+3a_n)/(3+2a_n),ngeq1,a n dif("lim")_(nvecoo)a_n=a , then find the value of adot

If a_1=1a n da_(n+1)=(4+3a_n)/(3+2a_n),ngeq1,a n dif("lim")_(nvecoo)a_n=a , then find the value of adot