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

lim_(x rarr oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^(-1){((2x+1)/(x-1))^(x))) 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)

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

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

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

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

lim_(x rarr oo){sqrt(x+1)-sqrt(x)}sqrt(x+2)