## anonymous one year ago Continuity and One-sided limits

1. anonymous

$\lim_{x \rightarrow 1} f(x) (1- ||-\frac{ x }{ 2 }||)$

2. anonymous

3. anonymous

thanks

4. 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?

5. anonymous

here let me take a pic of the problem in my textbook

6. 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")

7. anonymous

oh, it is just 1

8. anonymous

Okay, cool.

9. anonymous

Well, were taking the limit as x gets close to 1. So let's stick that into the equation.

10. anonymous

http://i.imgur.com/hlnt6Lg.jpg number 26

11. anonymous

i would get 1 1/2 ?

12. anonymous

Well, the bit inside the ||#|| symbol should always be positive, right?

13. anonymous

I mean, it's an absolute value symbol, if I understood right. So ||5|| = +5, and ||-7|| = +7.

14. anonymous

In this case, you'd want ||-x/2|| to be positive

15. anonymous

Did you click the link? it isn't an absolute value sign

16. anonymous

17. anonymous

its alright, kinda hard to input calc equations through text, not all the symbols are included

18. anonymous

Looks like it's the floor function then, which takes whatever is inside it and rounds it down to the nearest integer.

19. 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?

20. anonymous

how does -1/2 become 1 instead of 0?

21. 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?

22. 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?

23. anonymous

24. 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.

25. anonymous

Sorry! :(