Continuity test for mod x function

[Qwertyuiop[]]

Hi, I have a question regarding the continuity of the mod x function. |x| is a continuous function but when we take the limits when x<0 x=0 and x>0, we get different values , so why it's still a continuous function? I don't understand.

 

[Dr.Peterson]

Hi, I have a question regarding the continuity of the mod x function. |x| is a continuous function but when we take the limits when x<0 x=0 and x>0, we get different values , so why it's still a continuous function? I don't understand.

Please show your work in taking those limits. I suspect you didn't do what you say you did, or what is relevant to continuity.

 

[Qwertyuiop[]]

Please show your work in taking those limits. I suspect you didn't do what you say you did, or what is relevant to continuity.

my fault, i was using the differentiability test . I get it now. The limit of f(x) for x<0 and x>0 = f(0). ?

 

[Dr.Peterson]

my fault, i was using the differentiability test . I get it now. The limit of f(x) for x<0 and x>0 = f(0). ?

That is one of the possibilities I had in mind.

But still, what do you mean by "The limit of f(x) for x<0"? That sounds like you are taking the limit as x approaches some negative value.

Probably what you mean is "the limit of f(x) as x approaches 0 from below". You need to say what you mean in mathematics!

 

[Qwertyuiop[]]

That is one of the possibilities I had in mind.

But still, what do you mean by "The limit of f(x) for x<0"? That sounds like you are taking the limit as x approaches some negative value.

Probably what you mean is "the limit of f(x) as x approaches 0 from below". You need to say what you mean in mathematics!

yes, that's what I meant to say