Discuss the continuity of `f(x)=sgn(2cosx-1)`

Discuss the continuity of f(x)=sgn(x^3-x)

Discuss the continuity of f(x)=sgn(x^2-2x+3)

Discuss the continuity of f(x)=(log|x|)sgn(x^2-1),x!=0.

Discuss the continuity of f(x)={1/(e^(x-1)),x!=1 0,x=1

Discuss the continuity of f(x)=[tan^(-1)x]([dot] represents the greatest integer function).

f(x)={|x+1|;xlt=0x ;x >0 and g(x)={|x|+1;xlt=1-|x-2|;x >1 Draw its graph and discuss the continuity of f(x)+g(x)dot

Discuss the continuity of f(x)=(lim)_(nvecoo)(x^(2n)-1)/(x^(2n)+1)

Discuss the continuity of f(x)={(x^2)/(|x|),x!=0 0,x=0

Discuss the continuity of f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)|),x!=1,2, 6,x=1, 12 ,x=2

Draw the graph and discuss the continuity of f (x) = [sin x + cos x], x in [0, 2pi), where [.] represents the greatest integer function.