`sqrt((3x-1)/(2-x))>1`

(d)/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]=(1)/(2(1+x)sqrt(x)) (b) (3)/((1+x)sqrt(x))(2)/((1+x)sqrt(x)) (d) (3)/(2(1+x)sqrt(x))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]= (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]= 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

If f(x)=sin^(-1)((sqrt(3))/(2)x-(1)/(2)sqrt(1-x^(2))),-(1)/(2)<=x<=1, then f(x) is equal to

Evaluate: ("lim")_(xvecoo)(sqrt(3x^2-1)-sqrt(2x^2-1))/(4x+3)

lim_(xrarr oo)(sqrt(3x^2-1)+sqrt(2x^2-1))/(4x+3)=

Evaluate: ("lim")_(xvecoo)(sqrt(3x^2-1)-sqrt(2x^2-1))/(4x+3)

The domain of definition of the function f(x)=sqrt(3-2^(x)-2^(1-x))+sqrt(sin^(-1)x) is