`T h e d o m a i n o ff(x)=cos^(- 1)(2/(2+sinx)) in [0, 2pi]i s[0,pi/2]2)[pi/2,pi]`

Range of the function f(x)=(cos^(-1)abs(1-x^(2))) is a. [0,pi/2] " " b. [0,pi/3] c. (o,pi) " " d. (pi/2,pi)

Let the function f'(x)=sin x be one- one and onto. Then a possible domain of f is O [0,2 pi] O [0,pi] O [-(pi)/(2),(pi)/(2)] O [-pi, pi]

Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,pi),i s-1 (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,2pi),i s1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (-pi/2,pi/2),i s-1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (pi/2,(3pi)/2),i s-1

Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,pi),i s-1 (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,2pi),i s1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (-pi/2,pi/2),i s-1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (pi/2,(3pi)/2),i s-1

Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,pi),i s-1 (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,2pi),i s1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (-pi/2,pi/2),i s-1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (pi/2,(3pi)/2),i s-1

Differentiate the following function with respect to x : sin^(-1)(sinx),x in [0,2pi] cos^(-1)(cosx),x in [0,2pi] tan^(-1)(tanx),x in [0,pi]-{pi/2}

One of the root equation cos x-x+(1)/(2)=0 lies in the interval (0,(pi)/(2))(b)(-(pi)/(2,0))(c)((pi)/(2),pi)(d)(pi,(3 pi)/(2))

The range of the function f(x)=int_(-1)^1(sinxdt)/((1-2tcosx+t^2)i s (a) [-pi/2,pi/2] (b) [0,pi] (c) {0,pi} (d) {-pi/2,pi/2}

Find the number of solution(s) of the following questions (a) x^2 + x + 1 + sinx = 0, x in [0, 2pi] (b) x^2 + x + 1 + sinx = 0, x in [pi, 2pi] (c) x^2 + x + sinx = 0, x in [0, pi]