`underset(x to oo)lim ((x^(3))/(3x^(2)-1)-(x^(2))/(3x+1))=`

underset(x to oo)lim (3x^(3)+x^(2)-1)/(x^(2)-x+7)=

underset(x to oo)lim (|3x^(2)+1|)/(2x^(2)+1)=

Find the limits : (a) underset(x to oo)lim ((2x^(2)+3)/(2x^(2)+5))^(8x^(2)+3) (b) underset(x to 0)lim ((1+tan x)/(1+tan x))^(1//sin x) (c ) underset(x to 1)lim (1+sin pi x)^(cot pi x) (d) underset(x to a)lim ((sin x)/(sin a))^(1//(x-a)) (a ne kpi," with k integer")

underset(x to oo)lim (3x^(2)+5x+2)/(2x^(2)-3x+1)=

underset(x to oo)lim ((x+1)(2x+3))/((x+2)(3x+4))=

Find the limits : underset(x to oo)lim ((1+x)/(2+x))^((1-sqrtx)//(1-x)) (b) underset(x to oo)lim ((x^(2)+2x-1)/(2x^(2)-3x-2))^((2x+1)//(x-1))

Find underset(x to oo)lim (1+1/x^2)^x

underset(n to oo)lim (3^(x+1)+4)/(3^(x+2)+4)=

underset(x to oo)lim x^(3//2) (sqrt(x^(3)+1)-sqrt(x^(3)-1))=