If `f(x)=x/(sinx)a n dg(x)=x/(tanx),w h e r e0ltxlt=1,` then in this interval

f(x)=(x)/(sinx ) and g(x)=(x)/(tanx) , where 0 lt x le 1 then in the interval

y=e^(sinx)+(tanx)^(x)

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 nx!=0 1,w h e nx=0dot Find whether f(x) is continuous at x=0

Find the following function is differentiable at a given point or not? f(x)=[x\ sinpix]a t\ x=0,\ w h e r e\ [x] denotes the greatest integer less than or equal to x .

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

If f(x)={((tanx)/(sinx)",", x ne 0),(1",", x =0):} then f(x) is

If f(x)={("sin"[x])/([x]),for[x]!=0 0,for[x]=0,w h e r e[x] denotes the greatest integer less than or equal to x , then ("lim")_(xvec0)f(x) is 1 (b) 0 (c) -1 (d) none of these

Let f(x)=(sqrt(1+sinx)-sqrt(1-sinx))/(tanx) , x ne 0 Then lim_(x to 0) f(x) is equal to

Let f(x)=x-[x], for ever real number x ,w h e r e[x] is the greatest integer less than or equal to xdot Then, evaluate int_(-1)^1f(x)dx .