The value of `lim_(xto1^(+))(int_(1)^(x)|t-1|dt)/(sin(x-1))` is

Let f : R to R be a differentiable funcation and f (1) = 4 . Then , the value of lim_(xto1) int_(4)^(f(x))(2t)/( x-1) dt is

The value of Lim_(x->0^+)(int_1^cosx(cos^-1t)dt)/(2x-sin(2x)) is equal to

The value of lim_(xto2)int_(2)^(x)(3t^(2))/(x-2)dt is

The value of lim _( x to 0^(+))(int _(1)^(cos x) (cos ^(-1) t )dt)/(2x - sin 2x) is equal to:

The value of lim_(xto0)(1)/(x) int_(0)^(x)(1+ sin 2t)^(1/t) dt equals :

The value of lim_(xto0)(1)/(x) int_(0)^(x)(1+ sin 2t)^(1/t) dt equals :

The value of lim_(x rarr0^(+))(int_(1)^(cos x)(cos^(-1)t)dt)/(2x-sin(2x)) is equal to

The value of lim_(xto1^(-)) (1-sqrt(x))/((cos^(-1)x)^(2)) is