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

Evaluate : lim_( x -> 0 )( ( 1-x ) ^( 1/n ) -1) /x =

Evaluate lim_(x to 0) (1 - x^(n) - 1)/(x)

If I_n=int_0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ("lim")_(nvecoo)I_ndot (a)0 (b) 1 (c) 2 (d) 1/2

Evaluate :(lim_(x rarr oo))_(x rarr oo)(1)/(1+n^(2))+(1)/(2+n^(2))+...+(n)/(n+n^(2))

Evaluate: Lim_(n rarr oo)[[1,x/n],[-x/n,1]]^(n)

Find the values of a if f(x)=(lim)_(n rarr oo)(ax^(2n)+2)/(x^(2n)+a+1) is continuous at x=1

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

lim_ (x rarr1) (lim_ (n rarr oo) [n ^ (2) (x ^ ((1) / (n)) - x ^ ((1) / (n + 1))) / (x ^ ( 3) -1)])

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

Evaluate lim_(xto1)(x+x^(2)+…….+x^(n)-n)/(x-1)