Question

Limits!!

Answer 1

I doubt if it exists

Answer 2

So approaching from the left, we'll use the part of the function that defined for \(\large x<0\)

\[\large f(0^-)=5(0^-)-9\]We're approaching -9 from the left.

How bout from the right?
Weeeelll, we'll use the part of the function that is defined for \(\large x\ge0\)

\[\large f(0^+)=|2-(0^+)|\]
It appears we're approaching 2 when we approach x=0 from the right.

Since the left and right limits do not agree, what does that tell us? :O

Answer 3

I hope I didn't confuse you with the weird notation. :) lol

Answer 4

Maybe this would have been a little clearer.\[\large f(x)=5x-9 \qquad\text{for}\qquad x\lt 0\]\[\large f(x)=|2-x| \qquad\text{for}\qquad x\ge0\]

Answer 5

Like i said o.O

Answer 6

wait so normally how would I find the limit of this??? or tell if it exists or not?! :)sorry @zepdrix this is confusin :(

Answer 7

Piece-wise functions are a little weird.
You can think of them as 2 different functions.

It's one function when you're dealing with certain x values.
Then it's something totally different when dealing with other x values.

So we have the function,\[\large f(x)=5x-9\]when our x is less than zero.

Taking the limit from the left,\[\large \lim_{x\to0^-}f(x)=-9\]

Understand that part? :o

Answer 8

If we're approaching from the left, then x is less than 0.
That's why we use this part of the function.

Grrr you ran off again +_+ lol

Answer 9

okay!! :D so since x is -9 we are using this part of the function ight??? XD ahhh man I'm here, I'm here!!!! :)sorry :( @zepdrix

Answer 10

no, since x is less than 0, we're using this part of the function.

\[\Large \lim_{x\to0^-}\]This notation means, approach zero from the left side.
Meaning that our x is less than 0.

Answer 11

ok cool :D

Answer 12

The piece-wise function is telling us,


if our x is less than 0, our function is\[\large f(x)=5x-9\]

if our x is greater than or equal to 0, then our function is\[\large f(x)=|2-x|\]

Answer 13

ok cool I got that part :)

Answer 14

It's a lil tricky to get used to :O
What you're basically trying to show here is

The limit from the left = something
the limit from the right = something else.

Since the left and right limits are not the same, then the limit does not exist.

If,
\[\Large \lim_{x\to0^-}f(x)\ne\lim_{x\to0^+}f(x)\]
Then,\[\Large \lim_{x\to0}f(x)=DNE\]

Answer 15

oh wait so basically it's showing the equations from both the left and right (since below 0 is neg and above pos) and it wants me to see if they have the same limits?

Answer 16

yes.

Answer 17

okso if they had the same limits that would be the answr? but since they have different limits it's doe not exist?

Answer 18

Correct :)
If they had given us the same value from the left and the right, that would be our limiting value.

Different is bad D:

Answer 19

DIFFERENT SUCKS xD LOLthank you @zepdrix :)))))))))! so what would be the easiest way in these type of questions do decide is their limits are the same or not??

Answer 20

Mmmmmmmmmmmm how bout an example :O

Answer 21

ok so like

Answer 22

Noooo XD My example! lol