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)=sgn(x^3-x)

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

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

Discuss the differentiability of f(x)={(sinx^2)/x ,x!=0 0,x=0a tx=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^2, x is rational -x^2,x is irrational

f(x)={|x+1|;xlt=0x ;x >0 and g(x)={|x|+1;xlt=1-|x-2|;x >1 Draw its graph and discuss the continuity of f(x)+g(x)dot

If f(x)={x-2, x le 0 and 4-x^2,x > 0, then discuss the continuity of y=f(f(x)).

Discuss the differentiability of f(x)=|x^3| at x=0