7. Find `lim_(x->oo) (x^3+x^2+1)/(x^3-x^2+1)`

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

Evaluate the following limit: (lim)_(x->1)(x^4-3x^3+2)/(x^3-5x^2+3x+1)

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

The value of lim_(xrarr oo) (3sqrt(x^3+x^2)-3sqrt(x^3-x^2)) , is

lim_{x \to 1} (3x-1)^2/(x+1)^3

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

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

Evaluate the following limits : Lim_(x to oo) (x^(3)+6x^(2)+1)/(x^(4)+3)

If lim_(x->oo) f(x) exists and is finite and nonzero and if lim_(x->oo) {f(x)+(3f(x)−1)/(f^2(x))}=3 ,then the value of lim_(x->oo) f(x) is

Evaluate the following limits : Lim_(x to 1) (x^(4) - 3x^(3) +2)/(x^(3)-5x^(2)+3x+1)