`lim_(x->oo) (cot^-1(sqrt(x+1)-sqrtx))/(sec^-1{((2x+1)/(x-1))^x)}` is equal to

lim_(xrarroo) (cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x-1))^(x)})=

lim_(xrarroo) (cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x-1))^(x)})=

lim_(xrarroo) (cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x-1))^(x)})=

lim_(x->oo) (x-sqrt(x^2-1))

underset(xrarroo)(lim)(cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x-1))^(x)})=

underset(xrarroo)(lim)(cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x-1))^(x)})=

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

lim_(x rarr oo) (sqrt(x+1)-sqrtx)sqrtx

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

lim_(x to oo) (sqrt(x + 1) - sqrt(x)) equals