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Statement 1: lim(x->oo)((1^2)/(x^3)+(2^2...

Statement 1: `lim_(x->oo)((1^2)/(x^3)+(2^2)/(x^3)+(3^2)/(x^3)+......+(x^2)/(x^3))=lim_(x->oo)(1^2)/(x^3)+lim_(x->oo)(2^2)/(x^3)+......+lim_(x->oo)(x^2)/(x^3)=0` Statement 2: `lim_(x->a)(f_1(x)+f_2(x)+...+f_n(x))=lim_(x->a)f_1(x)+lim_(x->a)f(x)+.....+lim_(x->a)f_n(x)`

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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.

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)((x^(2)+5x+3)/(x^(2)+x+3))^((1)/(x))

Statement 1: lim_ (x rarr oo) ((1 ^ (2)) / (x ^ (3)) + (2 ^ (2)) / (x ^ (3)) + (3 ^ (2)) / (x ^ (3)) + ...... + (x ^ (2)) / (x ^ (3))) = lim_ (x rarr oo) (1 ^ (2)) / (x ^ ( 3)) + lim_ (x rarr oo) (2 ^ (2)) / (x ^ (3)) + ...... + lim_ (x rarr a) (x ^ (2)) / (x ^ (3)) lim_ (x rarr a) (f_ (1) (x) + f_ (2) (x) + ... + f_ (n) (x)) = lim_ (x rarr a) f_ (1) (x) + lim_ (x rarr a) f (x) + ...... + lim_ (x rarr a) f_ (n) (x)

lim_(x rarr oo)(1+2+3+...+x)/(x^(2))

lim_(x rarr oo)(1+2+3+...+x)/(x^(2))

lim_(x rarr oo)((3x^(2)+1)/(2x^(2)-1))^((x^(3))/(1-x))

lim_(x rarr oo)((3x^(2)+1)/(2x^(2)-1))^((x^(3))/(1-x))

lim_(x rarr oo)(1+2+3+....+x)/(x^(2))

lim_(x rarr oo)(1+2+3+....+x)/(x^(2))