`lim_(x->0^-)([x]+[x^2]+[x^3]++[x^(2n+1)]+n+1)/(1+[x^2]+|x|+2x), n in N` is equal to

lim_(x rarr0^(-))([x]+[x^(2)]+[x^(3)]++[x^(2n+1)]+n+1)/(1+[x^(2)]+|x|+2x),n in N

lim_(n rarr oo)([x]+[3x]+[5x]+[(2n-1)x])/(n^(2))

If f(x)=lim_(n->oo)[2x+4x^3+6x^5++2n x^(2n-1)] (0ltxlt1) then int f(x)dx is equal to:

lim_(x rarr1)((x+x^(2)+x^(3)++x^(n))-n)/(x-1)

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_(x->0)((1^x+2^x+3^x+....+n^x)/n)^(1/x)

If lim _(xto1)(x^(1)+x^(2)+x^(3)+"..."+x^(n)-n)/(x-1)=820,(nin N) then the value of n is equal to

lim_ (n rarr oo) (1) / (2) tan ((x) / (2)) + (1) / (2 ^ (2)) tan ((x) / (2 ^ (2))). ... + (1) / (2 ^ (n)) tan ((x) / (2 ^ (n))) is equal to lim_ (n rarr oo) sum_ (n = 1) ^ (n) (1 ) / (2 ^ (n)) tan ((x) / (2 ^ (n)))