Discuss the continuity of `f(x)=sinx+cosx`

Discuss the continuity of f(x)=sinxcosx

Discuss the continuity of f(x)=sin|x| .

Discuss the continuity of f(x) =[x]

Discuss the continuity of f(x)=|sinx+cosx| at x=pi .

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

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

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

Discuss the continuity of f(x) = tan^(-1)x

Discuss the continuity of the cosine, cosecant, secant and cotangent functions: f(x)= cosx, x in R

Discuss the continuity of f(x) at x = 0 if : f(x)={{:((sqrt(1+x)-sqrt(1-x))/(sinx)", if "xne0),(1" , if "x=0):} .