`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_(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

f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then lim_(x to -3) ((x ^(2) +4x +3))/(sin (x+3) g (x)) is equal to:

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