Question

Continuity and One-sided limits

Answer 1

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

Answer 2

Hi, I can help you!

Answer 3

thanks

Answer 4

Just to check, first, is this meant to be a one-sided limit? And if so, which side of 1 are we approaching from?

Answer 5

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

Answer 6

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")

Answer 7

oh, it is just 1

Answer 8

Okay, cool.

Answer 9

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

Answer 10

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

Answer 11

i would get 1 1/2 ?

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

Oops, my bad!

Answer 17

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

Answer 18

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

Answer 19

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?

Answer 20

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

Answer 21

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?

Answer 22

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?

Answer 23

@BasketWeave

Answer 24

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.

Answer 25

Sorry! :(