Examine the origin for continuity & derivability in the case of the function f defined by `f(x)=xtan^(-1)(1/x), x!=0` and `f(0)=0`

Examine the origin for continuity G derivability in the case of the function f defined by f(x)=x tan^(-1)((1)/(x)),x!=0 and f(0)=0

Discuss the continuity of the function f defined f(x)=(1)/(x),x!=0

Discuss the continuity of the function defined by f(x)={x+2, if x 0

Examine for continuity and differentiability the points x=1 and x=2, the function f defined by f(x)=[{:(X[X],",",0leX where[X]=greatest integer less than or equal to x.

Find the value of a' for which the function f defined by f(x)={a(sin pi)/(2)(x+1),quad x 0 is continuous at x=0

Examine whether the function f given by f(x)=x^(2) is continuous at x=0

Examine the continuity of the function f(x) at x=0 for f(x)=x/(2|x|) where x!=0

Test the continuity of the following function at the origin; f(x)={(x)/(|x|),x!=0 and 1,x=0

Check the continuity of the following functions: f(x){(1)/(1-e^((1)/(x))),x!=0 and 0,x=0