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

lim_(x rarr oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(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_(x->oo) (x-sqrt(x^2-1))

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

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

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

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

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

lim_(x rarr oo)sec^(-1)((x)/(x+1)) is equal to:

Which of the following is/are true? (a) lim_(x rarr oo)((2+x)^(40)(4+x)^(5))/((2-x)^(45))=1(b)lim_(x rarr0)(1-cos^(3)x)/(x sin x cos x)=(3)/(2)(c)lim_(x rarr0)(ln(1+2x)-2ln(1+x))/(cot^(-1)(sqrt(x+1)-sqrt(x)))=-1 (d) lim_(x rarr oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^(1)((2x+1)/((x-1)^(2)))=1)=-1 (d)