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

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.

"lim_(x rarr oo)(1)/(x^(2))

lim_(x->oo) (x-sqrt(x^2-1))

lim_(x rarr oo)(1)/(x^(2))

lim_(x rarr oo)(1)/(x^(2))

Fill in the blanks: lim_(x rarr oo) ((x^2+1)/(x^2-1))^(x^2) =_______

lim_ (x rarr oo) (1+ (2) / (x)) ^ (x)

Lim_(x->oo) (2x - 1)/(x + 2)

lim_(x rarr oo)(2-(1)/(x)+(4)/(x^(2)))

lim_ (x rarr oo) ((1) / (x ^ (2)) + (2) / (x ^ (2)) ++ (x) / (x ^ (2)))