6.find `lim_(x->o)((x^2+2)/(2x^2+1))^(x^2)`

lim_(x->0)(1/(x^2)-1/(tan^2x))

Evaluate lim_(xto0)((1+5x^(2))/(1+3x^(2)))^(1//x^(2))

Evaluate lim_(xtooo) ((7x^(2)+1)/(5x^(2)-1))^((x^(5))/(1-x^(3))).

find lim_(x->1) ((x^4-3x^2+2)/(x^3-5x^2+3x+1))

Evaluate: lim_(x->oo)((x^2+x-1)/(3x^2+2x+4))^((3x^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.

Evaluate the limit: lim_(x->1)((2x-3)(sqrt(x)-1))/(2x^2)

Evaluate the following: lim_(xto1/3)(3x^2+5x-2)/(9x^2-1)

Evaluate the following limit: (lim)_(x->2)(1/(x-2)-4/(x^3-2x^2))\ \

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