Question

discuss the continuity of modulus of x or |x| .​

Answer 1

Answer:

f( x)= - x, x<0

f(x)= x,x>=0

let us check the continuity at x=0

LHL = lim x tends to a minus f ( x)

= lim x 0 (- x )

=-0

=0

RHL = lim x tends to a plus f( x)

= lim x 0 ( x)

=0

f(x) =0

=0

here LHL= RHL= f(x)

so the given function is continous at x=0

Answer 2

Answer:

the function |x| is continuous everywhere and not differentiable at zero