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

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

Discuss the continuity of f(x)={|x|cos(1/x),\ \ \ x!=0 0,\ \ \ \ x=0 at x=0

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

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

Discuss the continuity of f(x) ={:{((sin^2 2x)/(x^2)", "x ne 0),(1", " x= 0):}, at x=0.

Discuss the continuity of f(x) ={:{(cos""(1)/(x)", "x ne 0),(" "1", " x= 0):},

Discuss the continuity of f(x) ={:{(sin""(1)/(x)", "x ne 0),(" "1", " x= 0):},

Discuss the continuity of f(x)={(x-a)sin(1/(x-a)),\ \ \ x!=a\ \ \ \ \ \ \ \ \ \ \ \ 0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=a at x=a

Let f(x)={(1+3x)^(1/x),x!=0 and e^3,x=0. Discuss the continuity of f(x) at (a)x=0, (b) x=1.

Let f(x)={(1+3x)^(1/x), x != 0e^3,x=0 Discuss the continuity of f(x) at (a) x=0, (b) x=1