anonymous
  • anonymous
Continuity and One-sided limits
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[ \lim_{x \rightarrow 1} f(x) (1- ||-\frac{ x }{ 2 }||)\]
anonymous
  • anonymous
Hi, I can help you!
anonymous
  • anonymous
thanks

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anonymous
  • anonymous
Just to check, first, is this meant to be a one-sided limit? And if so, which side of 1 are we approaching from?
anonymous
  • anonymous
here let me take a pic of the problem in my textbook
anonymous
  • anonymous
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")
anonymous
  • anonymous
oh, it is just 1
anonymous
  • anonymous
Okay, cool.
anonymous
  • anonymous
Well, were taking the limit as x gets close to 1. So let's stick that into the equation.
anonymous
  • anonymous
http://i.imgur.com/hlnt6Lg.jpg number 26
anonymous
  • anonymous
i would get 1 1/2 ?
anonymous
  • anonymous
Well, the bit inside the ||#|| symbol should always be positive, right?
anonymous
  • anonymous
I mean, it's an absolute value symbol, if I understood right. So ||5|| = +5, and ||-7|| = +7.
anonymous
  • anonymous
In this case, you'd want ||-x/2|| to be positive
anonymous
  • anonymous
Did you click the link? it isn't an absolute value sign
anonymous
  • anonymous
Oops, my bad!
anonymous
  • anonymous
its alright, kinda hard to input calc equations through text, not all the symbols are included
anonymous
  • anonymous
Looks like it's the floor function then, which takes whatever is inside it and rounds it down to the nearest integer.
anonymous
  • anonymous
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?
anonymous
  • anonymous
how does -1/2 become 1 instead of 0?
anonymous
  • anonymous
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?
anonymous
  • anonymous
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?
anonymous
  • anonymous
@BasketWeave
anonymous
  • anonymous
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.
anonymous
  • anonymous
Sorry! :(

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