Question

Use the given graph to determine the limit, if it exists.

Answer 1

Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x.

Answer 2

there is no reason for one-sided limit not to exist.

Answer 3

so that means there would be a limit.....and in case I don't respond for the next few minutes, Im going to the bathroom I really have to pee:p

Answer 4

yes.

Answer 5

me too!

Answer 6

one sides limits, (both) exist.

Answer 7

But can you tell me what they are, though, please?

~ \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~2^-}f(x)}\) =?

~ \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~2^+}f(x)}\) =?

Answer 8

im back! lol
but the question begins with Use the given graph to determine the limit, if it exists.
then it shows the graph that I attached
and after that it says \[\lim_{x \rightarrow 2-} f(x) \lim_{x \rightarrow 2+}f(x)\]

Answer 9

(you can use ~ as a space. ~~ would be more space, on on)

Answer 10

what are you trying to say, I am not getting you, sorry.

Answer 11

you are right that they exist, but I just wanted you, if you don't mind, to tell me what the limits (both of them) are/were.

Answer 12

and by the way, the latex for in-text limits, integrals, and sigmas.

you can use my latex.
`\(\large\color{black}{\displaystyle\lim_{x \rightarrow ~a}f(x)}\)` LIMIT
\(\large\color{black}{\displaystyle\lim_{x \rightarrow ~a} f(x)}\)



`\(\large\color{black}{\displaystyle\int\limits_{~}^{~}f(x)~dx}\)` INTEGRAL
\(\large\color{black}{\displaystyle\int\limits_{~}^{~}f(x)~dx}\)


`\(\large\color{black}{ \displaystyle \sum_{ n=1 }^{ \infty } ~ f(n)}\)` SIGMA
\(\large\color{black}{ \displaystyle \sum_{ n=1 }^{ \infty } ~ f(n)}\)

Answer 13

well its just that im not wuite sure on how to find a limit by looking at a graph. so I was wondering if you could tell me how I could read this graph for looking at limits:)

Answer 14

okay, see where the function is going from the left side?
See it hitting a point (open dot) (\(\normalsize\color{blue}{ 2 }\),\(\normalsize\color{red}{ \rm 4 }\)) ?

that means that: \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~\color{blue}{2}^-}f(x)=\color{red}{4}}\)

Answer 15

ok, then would the second limit be -1?

Answer 16

tyes.

Answer 17

and f(4) = 1

Answer 18

I mean f(2)=4, excuse me

Answer 19

so my answer would be 4;-1?
here are the answer choices:
A) 1;1
B) -1; 4
C) 4; -1
D)DOES NOT EXIST; DOES NOT EXIST

Answer 20

the first number is what the left side of the limit approaches, and the second is what the right side of the limit approaches.

Answer 21

go ahead and type, please, don't feel like you are interrupting me or anything of this sort.

Answer 22

and this is where there is discontinuity.

1) \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~2}f(x)}\) DNE

2) (certainly that) \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~2}f(x)\ne f(2)}\) ( f(2)=4 )

Answer 23

the only condition we have is that f(2) exists, but that is not enough for it to be continuous.

Answer 24

of course! I just have to refresh the page each time I need to respond for some reason so I just wanna let you know that im paying attention and basically refreshing the page each time i need to respond:)
and ok....im still not understanding this:/ how exactly do i solve this?

Answer 25

if you post button is hiding, then just press Tab+enter when you are done typing. (no need refreshing if that's the concern)

Answer 26

*your post...

Answer 27

ok thanks:)

Answer 28

by the way, f(2) =1, not 4, as I said.

Answer 29

the discontinuity is still same.

Answer 30

we just look at the graph...
and we see that as we go from the right, we hit a white dot (2,-1)
and we see that as we go from the left, we hit a white dot (2,4)

Answer 31

ok...where do i go from there?

Answer 32

that gives us:

\(\large\color{black}{\displaystyle\lim_{x \rightarrow ~2^-}f(x)=4}\)

\(\large\color{black}{\displaystyle\lim_{x \rightarrow ~2^+}f(x)=-1}\)

Answer 33

do you mind if I spend some time labeling a picture?

Answer 34

no problem! but i have to shower and then head out because i have to go to my sat class:( so i might come back on at around 8-9 pm....and its 3 rn where i live

Answer 35

the red is, \(\large\color{red}{\displaystyle\lim_{x \rightarrow ~2^{-}}f(x)}\)

the green is, \(\large\color{green}{\displaystyle\lim_{x \rightarrow ~2^{+}}f(x)}\)

the blue is, \(\large\color{blue}{f(2)}\)