" (vi) "lim_(x rarr oo)(cos sqrt(x+1)-cos sqrt(x))

lim_(x rarr oo)((cos x)/x)

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

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

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_(x rarr oo)(sqrt(x^(2)+x+1)-sqrt(x^2+1))

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

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

lim_(x rarr oo)sqrt(x)(sqrt(x)-sqrt(x-a))

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

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