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

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

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

Discuss the conttinuity of f(x) ={{:((x-1)/(e^((1)/(x-1))),x=0),(0,x=0):} at x=1.

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

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.

Discuss the continuity of f(x)={2x-1,\ \ \ x<0 ; {2x+1,\ \ \ xgeq0 at x=0

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

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

Let f(x) ={{:(1+x,0lexle2),(3-x,2ltxle3):} then discuss the continuity of g(x) =f(f(x)).