Question

Find limit as x approaches three from the right of f of x..

Answer 1

The answers are:
-1
7
-4
Doesn't exist

I think that it's -4. Is that right?

Answer 2

please note that, you function can not to be made continuous at x=3!

Answer 3

Okay, so is my answer wrong? @Michele_Laino

Answer 4

yes I think!

Answer 5

If it's not -4, then is it -1?

Answer 6

no I think not!

Answer 7

Hmm, 7?

Answer 8

no I think not!

Answer 9

I don't understand. Does the limit not exist? Because I thought it was -4.

Answer 10

I think, that your limit doesn't exist, because there is no way to make your function continue at x=3

Answer 11

1) What is \(\Large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{-}}~f(x)}\) ?

2) What is \(\Large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{+}}~f(x)}\) ?

Answer 12

When the sides are not equivalent than the limit DNE, but in your case are they equivalent or not?

Answer 13

\(\Large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{+}}~f(x)}\)

Answer 14

I am putting up more and more stuff, but can you just tell me if you

know what it means to say: \(\Large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{+}}~f(x)}\) ?

Answer 15

Yes?

Answer 16

Okay do you see this on the graph, do you see the point, where the function is approaching FROM THE RIGHT the point, whose x-coordinate is 3.
(there are 3 points/dots with x -coordinate 3, but tell me the one that is connected to the RIGHT part of your function)

Answer 17

It's -4

Answer 18

I'l;l put up an attachment for you to better see if you want

Answer 19

Yes, -4

Answer 20

So, \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{+}}=-4}\)

Answer 21

Thank you. I thought I was going crazy for a second.

Answer 22

No, it is just a need of looking.
can you tell me what \(\large\color{blue}{\displaystyle\lim_{x \rightarrow ~3^{-}}f(x)}\) is going to be?

Answer 23

Would it be 7?

Answer 24

sorry I'm not sure that your limit = -4, is not the right answer! because I think that, observing your graph that f(3) = 7, and y=7 is an isolated point

Answer 25

No, Michele, the \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{+}}f(x)=-4}\) is correct.
The limit only, although, \(\large\color{black}{f(3)=7}\)

Answer 26

I think that if limit exists, then that limit has to be equals to 7, because with y=7, our function is continue in x=3

Answer 27

And sunshine,

When I say \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{-}}f(x)}\) I mean, what is the y-coordinate of the point connected to the left part of the function, where the (x-coordinate 3)?

Answer 28

Only have to have \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{}}f(x)=7}\) is \(\large\color{black}{f(x)}\) is continuous at x=3.

Answer 29

In this case none of the conditions are mat:

For it to be continuous at \(\large\color{black}{x=3}\).

1) \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{}}f(x)}\) Exists.

2) \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{}}f(x)=f(3)}\)

3) \(\large\color{black}{f(3)}\) exists --- the only condition that's there.

Answer 30

@SolomonZelman you are right! so requested limit is equal to 7

Answer 31

No

Answer 32

So the limit doesn't exist because both left and right don't match? One is -4 and the other is 7.

Answer 33

The requested limit is \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{+}}f(x)}\) where it APPROACHES x from the right, and
that is \(\large\color{black}{-4}\)/

Answer 34

please y=7 is an isolated point of the image of your function

Answer 35

I'm majorly confused. What is the limit?? @SolomonZelman

Answer 36

So, that is an f(3). But it not the LIMIT. You probably have learned calculus a long time ago, it would not be bad to rvw. By no means do I mean to be rude.

\(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{-}}f(x)=1}\)

\(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{+}}f(x)=-4}\)

\(\large\color{black}{f(3)=7}\)

this is what we have.

Answer 37

Ohh, the \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{-}}f(x)}\) is NEGATIVE 1

Answer 38

@SolomonZelman please is our function continue at x=3?

Answer 39

No

Answer 40

Of course not.

Answer 41

wrong answer sorry!

Answer 42

I am not mathematician, but this I do know. Tell me,

1) Does \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{}}f(x)}\) EXIST?

2) Does \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3^{-}}f(x)=-4}\) ?

Answer 43

I get it now. The answer I needed was -4. So thanks to the both of you.

Answer 44

you are confusing something overhere. it is x=3 where all the discontunuity mess is going on.

Answer 45

Yes, you need -4:) yw

Answer 46

We can go over this, Michelle, if you would like to.

Answer 47

@SolomonZelman last question, is x=3 an isolated point?

Answer 48

x=3 is not a point. the POINT on the function is \(\large\color{black}{(3,7)}\). Yes, it is isolated from the rest of the f(x).