Just a quickie (1 Viewer)

[Raginsheep]

Give two reasons explaining why y=|x|/x is not continuous when x=0. I can get reason 1 (you can't divide something by 0...well at least in 3u) but can't get the second reason.

 

[Xayma]

It isn't continuous as

Because it changes from 1 for x>0 to -1, x<0.

 

[ur_inner_child]

I know you're going to hate me for it but...

Thank god I don't do maths...

*dances*

 

[Raginsheep]

No it isnt.

Because it changes from 1 for x>0 to -1, x<0.

Umm....are you saying that "No it isnt" contunious or my reason wrong?

 

[aud]

I dunno... do the test for continuity?
The whole lim(x-> -0)f(x) = f(0) = lim(x-> +0)f(x)

Otherwise, I have no idea, and would just wing it

 

[Xayma]

Umm....are you saying that "No it isnt" contunious or my reason wrong?

Opps I had it was otherwise continuous, typed out what I was thinking.

 

[Raginsheep]

Acutally I'd say that thats a pretty good answer. I'll give that one to my friend and see. Thanx aud.

 

[gordo]

(you can't divide something by 0...well at least in 3u).

when can u ever divide by zero?

 

[Raginsheep]

In 4u maths, you get to play around wif immaginary numbers so you get results for stuff like 1/0 and root (-1).

 

[gordo]

lol do u?
so wat does 1/0 = ?

 

[Raginsheep]

lol do u?
so wat does 1/0 = ?

"i" or something. But I haven't started imaginary numbers yet cause im still stuck in the limbo between yr 11 and 12 ><

 

[gordo]

ah ok
i did 4u maths
the root of -1 = i
1/0 is undefined in all facets of maths, its obliterates the fundemental logic laws of maths
i did my history extn project on zero too
beleive me, you will never do dividing by zero

 

[Archman]

na 1/0 is not anything, not in maths i know anyway.

 

[Raginsheep]

Hmmm........obviously im horribly wrong then but I always thought that 1/0 = somethin... oh wellz....

 

[Slidey]

f(x)=|x|/x is not continuous because you can't divide by zero, and absolute vale functions are not continuous.

So the two functions it is composed of a discontinuous:
y=|x|
w=1/x
f(x) is just y.w

 

[Raginsheep]

but isn't y=|x+3| continuous?

 

[gordo]

what does conintinous mean?

 

[Slidey]

Well, things like 1/0 have "applications" in straight lines like x=1.
The rise is infinite, but the run is zero. infinity/0. But that doesn't tell you much, since infinity is not a real number... nor an imaginary number. You might do transfinite arithmetic at university. Furthermore, inf/0 is naughty because you can't divide by zero.

 

[aud]

Good, Slide Rule, good...

No. Absolute values are not continuous at their peak... I forget why, but I know my Maths teacher drilled that into my head... maybe cause it doesn't fulfil the formula I wrote before...

But think, you def can't differentiate that point on an absolute value graph. And you can differentiate a graph if it IS continuous. Therefore... it's not continuous... ;D

 

[Slidey]

but isn't y=|x+3| continuous?

Hmm. I know it's not differentiable at x=3. I guess I made the assumption that that means it is discontinuous.

Continuous means that a line or curve has no breaks in it. for example the function y=x/x is discontinuous because at x=0, it is undefined, so there is a missing point when it is graphed.