If `x<0,t h e ntan^(-1)x` is equal to

If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sqrt(1+x^2)) -cos^(-1)1/(sqrt(1+x^2)) (d) -cos e c^(-1)(sqrt(1+x^2))/x

If -1 lt x lt 0 , then cos^(-1) x is equal to

If x lt 0 then tan^(-1)(1/x) equals

If -1lt x lt 0 then tan^(-1) x equals

If f(x)=(log)_x(log x),t h e nf^(prime)(x) at x=e is equal to (a) 1/e (b) e (c) 1 (d) zero

If f(x)=sin^(-1)((sqrt(3))/2x-1/2sqrt(1-x^2)),-1/2lt=xlt=1,t h e nf(x) is equal to

If f(x)=(log)_x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e (c) 1 (d) zero

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equal to (a) -cosx (b) -sinx (c) int_0^x(x-t)f(t)dt (d) 0

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(prime)(x)+f(x) is equal to a) -cosx (b) -sinx c) int_0^x(x-t)f(t)dt (d) 0

Let f (x)= {((1+ax )^(1//x), x lt 0),( ((x+c)^(1//3)-1)/((x+1)^(1//2) -1), x gt 0):}, is continous at x=0, then 3 (e ^(a)+b+c) is equal to: