Find `lim_(x->oo) (1/x^2+2/x^2+....+x/x^2)`

lim_(x->oo) xsin(2/x)

lim_(x->oo)(x^2 - sinx)/(x^2-2)

lim_(x->oo) (x-sqrt(x^2+x))

lim_(x->oo)2^xsin(a/2^x)

Statement 1: lim_(xto oo)(1/(x^(2))+2/(x^(2))+3/(x^(2))+…………..+x/(x^(2)))=lim_(xto oo)1/(x^(2))+………….+lim_(xto oo)x/(x^(2))=0 Statement 2: lim_(xtoa)(f_(1)(x)+f_(2)(x)+………..+f_(n)(x))=lim_(xtoa)f_(1)(x)+………….+lim_(xtoa)f_(n)(x) provided each limit exists individually.

Find the value of lim_(x->oo)(2-1/x+4/x^2)

8. lim_(x->oo)(sqrt(x^2+x)-x)

Solve lim_(x->oo) (x^2-4)/((x-2)^2.(x+7))

If lim_(x -> oo) (1 + a/x + b/x^2)^(2x)= e^2 then the values of a and b, are

lim_(x->oo) ((x^2-2x+1)/(x^2-4x+2))^x is equal to