Discuss the continuity of `f(x)={(x{x}+1 ,, 0lt=x<1),(2-{x} ,, 1lt=x<2):}` where `{x}` denotes the fractional part function.

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

A function f(x) is defined by, f(x) = {{:(([x^(2)]-1)/(x^(2)-1)",","for",x^(2) ne 1),(0",","for",x^(2) = 1):} Discuss the continuity of f(x) at x = 1.

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

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

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

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

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

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

Discuss the continuity of the function f(x)= {(x , 0 le x lt1/2 ),( 12,x=1/2),( 1-x , 1/2ltxle1):} at the point x=1//2 .

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