`lim_(x->oo)[((x+a_1)(x+a_2)...........(x+a_n))^(1/n)-x]`

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

If 1<=m<=n,m in n, then the value of lim_(x rarr oo)(x_(1),x_(2)......x_(n)) is

if f(x) = (x - a_1) (x - a_2) .....(x - a_n) then find the value of lim_(x to a_1) f(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 a_1. a_2 ....... a_n are positive and (n - 1) s = a_1 + a_2 +.....+a_n then prove that (a_1 + a_2 +....+a_n)^n ge (n^2 - n)^n (s - a_1) (s - a_2)........(s - a_n)

If a_1, a_2,a_3,..........., a_n be an A.P. of non-zero terms, prove that : 1/(a_1 a_2)+1/(a_2 a_3)+ ............. + 1/(a_(n-1) a_n)= (n-1)/(a_1 a_n) .

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

Let a_1 , a_2 ... . . a_n be fixed real numbers and define a function f(x)= (x -a_1 )(x-a_2 )...(x -a_n). What is lim_(x rarr a_1)f(x) ? For some a ne a_1,a_2,....a_n , compute lim_(x rarr a)f(x) .

Let a_1,a_2,.....,a_n be fixed real numbers and define a function f(x) = (x-a_1) (x-a_2).....(x-a_n) . What is (lim)_(x->a_1)f(x) ? For some a!=a_1,a_2,.....,a_n , compute (lim)_(x->a)f(x)