If `f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1,` then in this interval

Discuss monotonocity of f(x)=x/(sinx)a n d g(x)=x/(tanx),w h e r e

Let f(x)=(sinx)/x and g(x)=|x.f(x)|+||x-2|-1|. Then, in the interval (0,3pi) g(x) is :

Statement 1: f(x)=cos x is continous at x=0a n dg(x)=[tanx],"w h e r e"[dot] represents greatest integer function, is discontinuous at x=0,t h e nh(x)=f(x)dotg(x) is discontinuous at x=0. Statement 2: If f(x) is continous and g(x) is discontinuous at x=a ,t h e nh(x)=f(x)g(x) is discontinuous at x=a

If f(x)={(sin3x)/x ,\ \ \ w h e n\ x!=0 1,\ \ \ w h e n\ x=0 . Find whether f(x) is continuous at x=0 .

If f(x)=(sin3x)/x,w h e nx!=0, f(x)= 1,w h e n x=0 Find whether f(x) is continuous at x=0

If f(x)=|x-2| a n d g(x)=f[f(x)],t h e n g^(prime)(x)= ______ for x>20

If f,\ g,\ h are real functions given by f(x)=x^2,g\ (x)=tanx\ a n d\ h(x)=log,\ x ,\ t h e n write the value of (hog\ of)(sqrt(pi/4))dot

Let f(x)=x^2 \ a n d \ g(x)=sinx for all x in R . Then the set of all x satisfying (fogogof)(x)=(gogof)(x),w h e r e (fog)(x)=f(g(x)), is

If F(x)a n dG(x) are even and odd extensions of the function f(x)=x|x|+"sin"|x+x e^x ,w h e r ex in (0,1),g(x)=cos|x|+x^2-x ,w h e r ex in (0,1) respectively to the interval (-1, 0)t h e nF(x)+G(x) in (-1,0) is (a). sin x+cos x+x e^(-x) (b)(sin x+cos x+x e^(-x)) (c)(sin x+cos x+x+x e^(-x)) (d)(sin x+cos x+x^2+x e^(-x))

If f''(x) gt forall in R, f(3)=0 and g(x) =f(tan^(2)x-2tanx+4y)0ltxlt(pi)/(2) ,then g(x) is increasing in