Discuss the continuity of the function fx=xx,x≠0 0 ,x=0 - Maths -

Question

Discuss the continuity of the function f x = x x , x ≠ 0
    0       , x = 0

Global Expert · Accepted Answer

Given: fx=xx, x≠00, x=0

x=x, x≥0-x, x<0⇒fx=1, x>0-1, x<00, x=0

We have
(LHL at x = 0) =
limx→0-fx=limh→0f0-h=limh→0f-h=limh→0-1=-1

(RHL at x = 0) =
limx→0+fx=limh→0f0+h=limh→0fh=limh→01=1

∴ limx→0-fx≠limx→0+fx

Thus, fx is discontinuous at x = 0

Discuss the continuity of the function f x = x x , x ≠ 0 0 , x = 0 .