`lim_(x rarr oo) ((x^5+2)^(1//4)-(x^2+1)^(1//3))/((x^4+2)^(1//5)-(x^3+1)^(1//2))=`

lim_(x rarr oo)(2x+1)/(3x-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 0)((5x^2+1)/(3x^2+1))^(1//x^2)

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

lim_(x rarr oo)tan^(-1)(x^(2)-x^(4))

lim_(x rarr oo)(sqrt(x^(2)+1)-(x^(2)+1)^((1)/(3)))/((x^(4)+1)^((1)/(4))-(x^(4)-1)^((1)/(5))) is equal to

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

Evaluate the following limits (if it exists) lim_(x rarr oo)(sqrt(x^(2)+1)-(x^(3)+1)^((1)/(3)))/((x^(4)+1)^((1)/(4))-(x^(5)+1)^((1)/(5)))

lim_(x rarr oo)((x^(2)+5x+3)/(x^(2)+x+3))^((1)/(x))