If `cos^(-1)(4x^3-3x)=a+bcos^(-1)x" for "-1 lt x lt -1/2,` then [a + b+ 4] is equal to {where [] denotes G.I.F}`

If f(x)=sin^(-1)x and lim_(xto1//2+)f(3x-4x^3)=a-3lim_(xto1//2+)f(x) , then [a] is equal to {where [] denotes G.I.F}

If f(x)=sin^(-1)x and lim_(xto1//2+)f(3x-4x^3)=a-3lim_(xto1//2+)f(x) , then [a] is equal to {where [] denotes G.I.F}

Discuss the continuity of f(x) in [0,2] where f(x) = {{:([cos pi x]" , " x le 1),(| 2x - 3 |.[ x- 2]" ," x gt 1):} where [.] denotes the G.I.F.

The number of points at which f(x)=[x]+|1-x|, -1lt x lt3 is not differentiable is (where [.] denotes G.I.F)

Lt_(x rarr4^(+))(x^(2)-7x+12)/(x-[x]) =[ where [ ] denotes G.I.F.]

If the function f(x)=cos^(-1)(x^((3)/(2))-sqrt(1-x-x^(2)+x^(3))) (" where, "AA 0 lt x lt 1), then the value of |sqrt3f'((1)/(2))| is equal to ("take "sqrt3=1.73)

If the function f(x)=cos^(-1)(x^((3)/(2))-sqrt(1-x-x^(2)+x^(3))) (" where, "AA 0 lt x lt 1), then the value of |sqrt3f'((1)/(2))| is equal to ("take "sqrt3=1.73)