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

f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then lim_(x to -3) ((x ^(2) +4x +3))/(sin (x+3) g (x)) is equal to:

lim_(x->oo)(e^(11x)-7x)^(1/(3x))

Evaluate the following limit: (lim)_(x->oo)((3x-1)(4x-2))/((x+8)(x-1))

lim_(x to oo)((5x^(2)-2)/(3x^(2)+8))=

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

The value of lim_(x->oo)(((x-1)(x-2)(x+3)(x+10)(x+15))^(1/5)-x) is ....

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

lim_(x->oo)((x^3)/(3x^2-4)-(x^2)/(3x+2)) is equal to (a) does not exist (b) 1//3 (c) 0 (d) 2/9

Which of the following is/are true? (a) lim_(x->oo)((2+x)^(40)(4+x)^5)/((2-x)^(45))=1 (b) lim_(x->0)(1-cos^3x)/(xsinxcosx)=3/2 (c) lim_(x->0)(ln(1+2x)-2"ln"(1+x))/(x^2)=-1 (d) lim_(x->oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^1((2x+1)/(x-1)^2)=1

Evaluate the following limits : Lim_(x to oo) (3x^(2)+x-1)/(x^(2)-x+7)