`lim_(x->oo){(3x^2+1)/(4x^2-1)}^(x^(3)/(1+x))`

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

Evaluate: lim_(x->oo) root(3)((x+1)(x+2)(x+3))-x

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

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: lim_(x->oo)x(tan^(-1)((x+1)/(x+4))-pi/4)

Evaluate: lim_(x->oo)x(tan^(-1)((x+1)/(x+4))-pi/4)

Let f(x)=lim_(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim_(x->oo) xf(x) (b) lim_(x->1) f(x) (c) lim_(x->0) f(x) (d) lim_(x->-oo) f(x)

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