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

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

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

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

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

Discuss the continuity of f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)|),x!=1,2, 6,x=1, 12 ,x=2

Discuss the extremum of f(x)=x^2+1/(x^2)

Discuss the continuity of f(x)=(lim)_(nvecoo)(x^(2n)-1)/(x^(2n)+1)

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

Discuss the extremum of f(x)=1/3(x+1/x)

Discuss the continuity of f(x)=[tan^(-1)x]([dot] represents the greatest integer function).