Continuity and One-sided limits

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Continuity and One-sided limits

Mathematics
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\[ \lim_{x \rightarrow 1} f(x) (1- ||-\frac{ x }{ 2 }||)\]
Hi, I can help you!
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Just to check, first, is this meant to be a one-sided limit? And if so, which side of 1 are we approaching from?
here let me take a pic of the problem in my textbook
Okay, sure. (If it's any easier, what I'm basically asking is whether there's a little + sign or a little - sign next to the "x->1")
oh, it is just 1
Okay, cool.
Well, were taking the limit as x gets close to 1. So let's stick that into the equation.
http://i.imgur.com/hlnt6Lg.jpg number 26
i would get 1 1/2 ?
Well, the bit inside the ||#|| symbol should always be positive, right?
I mean, it's an absolute value symbol, if I understood right. So ||5|| = +5, and ||-7|| = +7.
In this case, you'd want ||-x/2|| to be positive
Did you click the link? it isn't an absolute value sign
Oops, my bad!
its alright, kinda hard to input calc equations through text, not all the symbols are included
Looks like it's the floor function then, which takes whatever is inside it and rounds it down to the nearest integer.
so if x->1 then -x/2 becomes -1/2, which becomes -1 once you apply the floor function, and then you have 1 - (-1) which is 2. Does that sound sensible?
how does -1/2 become 1 instead of 0?
Looking at that photo again, I'm a bit confused because that notation is a bit different to what I normally use for the floor function. Maybe we want round-to-the-nearest-integer, rather than round-down-to-the-next-integer?
Is it because it is as x approaches 1 from the right and left, so i wouldn't include 0 or 2 ? other wise it would be, as x approaches 0 from the right and as x approaches 2 from the left right?
Hmm. I'm a bit confused, to be honest. I think I'd better admit that right now rather than accidentally give you the wrong answer.
Sorry! :(

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