Find limits graph

[forest epoch]

I need help with this question**.**

[light sequoia]

!status

[safe furnace]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[forest epoch]

step #1

[twin merlin]

what have you tried

[forest epoch]

puting in an answer, But i got it wrong**..**

[twin merlin]

Oh

I think I can't help but SWR can for sure!

[forest epoch]

huh?

who is SWR ?

[twin merlin]

I wouldn't talk like that

He is the most respected here in the server

[forest epoch]

im not sure who he is**..**

[twin merlin]

He asked you on what step you are

@light sequoia

[forest epoch]

Step #1

[twin merlin]

They doesnt seem to respond

[forest epoch]

oh**.**

[twin merlin]

Ok do you know what a limit is?

[forest epoch]

not really**..**

[light sequoia]

That would be a good start to find out. Do you have any notes or resources on it?

[forest epoch]

n**-no.**

[light sequoia]

In short, a limit examines what does a function look like as it's gets really close a certain point without actually getting to the exact point

[light sequoia]

How did you get assigned this problem without a book or notes to refer to?

[forest epoch]

idk**..** 😢

[light sequoia]

Do you understand this?

[forest epoch]

not really**..**

[light sequoia]

This is saying, what does the function's y value get really close to as its x value gets really close to -6

So here's the graph around -6

what is the y value approaching as the x value gets close to -6?

[forest epoch]

not sure**..**

[twin merlin]

do your finger

on the graph

and follow it

until 6

and look at the y-axis

at which y value would your finger be if you approach -6

[forest epoch]

im confused**..**

[uneven rapids]

Look at the x value “-6”

What y value is there when x = -6

That’s like the most basic way I can say it

[uneven rapids]

The x value…

When the line is at -6

What value is on the y axis

[light sequoia]

Do you know what we mean when we say "x value" and "y value"? Do you know what the x and y axes are?

[forest epoch]

sort of**..**

[uneven rapids]

Ok do you know where -6 is on the x axis?

[forest epoch]

y**-yes..**

[uneven rapids]

Do you see the line above -6?

[forest epoch]

yes**..**

[uneven rapids]

Imagine a straight line that goes from the line above -6 all the way to the y axis

What y axis value do you get? Closest to

[forest epoch]

4**?**

[uneven rapids]

That’s your answer

[twin merlin]

This is how you read the coordinates of a point

and as you approach x -> -6 the more you go near y -> 4

this is what I meant by following the graph with your finger

up until x = -6

so you get an idea of what approaching means

[forest epoch]

[twin merlin]

at least it's making you think, so I take that as progess as opposed to "I don't know"

[forest epoch]

im not sure on how to do this question**..**

[twin merlin]

notice

[tall flicker]

𝔸dωn𝓲²s

𝔸dωn𝓲²s

[uneven rapids]

I’ll go through the first one:
The first one is saying the limit as x approaches -6, from the left side. Look at the graph starting from the LEFT, and approach -6, what’s the value of the y axis when you approach from the left

[forest epoch]

[uneven rapids]

@forest epoch
You see the left side right?

[forest epoch]

yes**..**

[uneven rapids]

Do you see how x is -9, at the very left?

[forest epoch]

yes**..**

[uneven rapids]

Okay follow that line until it ends, you see how it ends up at -6?

[uneven rapids]

What y value is when the line gets to -6? Again create a straight line

[twin merlin]

i miss your anime gifs

[forest epoch]

im confused**..**

[forest epoch]

-4?

[uneven rapids]

Yes that’s from the left side

[forest epoch]

how would i find the next one**?**

i go eat now

brb

[forest epoch]

**-**7

[uneven rapids]

Yes

[forest epoch]

how would I solve this one**?**

[uneven rapids]

Since you have 2 different answers to where x approaches -6, the limit does not exist

[forest epoch]

how would I find this on a graph**?**

[uneven rapids]

f(-6) is just asking what the y coordinate is on the graph where it’s defined

And in this case it wants us to look at the closed circle, which = -4 on the y values

[forest epoch]

how would I solve this one**?**

[uneven rapids]

Okay I won’t be here to assist you for every problem

Just know when it says “x -> (“value”) it’s saying, when x that “value”, what is y

When x approaches 0 from the left side, y is -5

Another example is
lim f(x) x -> 0^+
What is y when x approaches 0 from the positive side? -5 again

Therefore the limit when x -> 0 converges to -5 and therefore does exist

I can’t walk you through it fully anymore, you have to try

I can answer questions

@forest epoch

[forest epoch]

ok**..**

[uneven rapids]

Sorry if I sounded mean but i can answer questions you have

[forest epoch]

ok**..**

[forest epoch]

wdym by when it "does exist" ?

[uneven rapids]

Limits can only exist if y is the same value when x approaches that number from both left side and right side

There are other scenarios where occasionally one-sided limits can exist but don’t worry about that

[uneven rapids]

If a limit is -5 from the left, and like -7 from the right, then it doesn’t exist

If it’s -5 from both left and right, it exists

[forest epoch]

so**..**

what if limit x → 0**?**

how would I solve that**?**

[uneven rapids]

This refers to the overall limit so on a graph, go to x = 0 and find what value “y” is when x is 0, when you find the line or point, identify if it approaches that same y value from both sides

[uneven rapids]

Example here for the first one:
lim: x -> 0^- means what value is y when x is 0? From the left (or negative side)
In this case, the answer is -5, since from the left side, the line approaches y = -5.

[forest epoch]

im confused**..**

[uneven rapids]

If you don’t mind me asking but what grade are you in?

because calculus could be pretty hard if you don’t know what I’m saying

or in school are you learning it?

[forest epoch]

12th grade**..**

[forest epoch]

i just started learning it in school**..**

i haven**'t learn this type of math before..**

[uneven rapids]

Oh

[forest epoch]

yeah**..**

[uneven rapids]

You know what the positive and negative sign above the zero mean right?

[forest epoch]

not sure**..**

[uneven rapids]

When it says 0+, it means 0 from the positive side (right, in red)

When it says 0-, it means 0 from the negative side (left, blue)

Do you understand?

[forest epoch]

i think so**..**

[uneven rapids]

Right now, just look at x -> 0 as x = 0
The question is asking, when x = 0 on the graph, what is y?

X is horizontal line, Y is vertical line

@forest epoch It may be confusing since 0 isn’t there on the horizontal line, but 0 is between -1 and 1, it’s the place where both lines intersect?

[forest epoch]

would it be does not exsit ?

[uneven rapids]

No the limit does exist

I made this

Green highlight = Y axis
Yellow highlight = X axis
When going along the yellow highlighted one, in the middle that’s where 0 is at, known as x = 0.

@forest epoch can I elaborate?

[forest epoch]

sure**.**

[uneven rapids]

Now that we know where x = 0 is, go along the green highlight (make sure x is still 0), when we go down, we see that the line goes to -5, this is called y = -5

We see that, when we go down on the y axis, we get -5

And as we can see, the line goes to y = -5 on both sides, so the limit does exist from the left and right side

[forest epoch]

wait**..** isnt left supposed to be ⬅️ and right would be ➡️ ?

[uneven rapids]

Yea the direction, but we’re calling “right” and “left” as points on the graph

Okay, the right side of the graph is everything above 0 (1 to 10)

And the left side is everything below 0 (-1 to -10)

So when we say “as x approaches 0 from the right side” we’re going from the right side until we reach x = 0, then after we stop and see if there is any y values on x = 0.

[uneven rapids]

Yes you got it

-10 -> 0 is left
+10 -> 0 is right

[forest epoch]

how would I find f(0)?

[uneven rapids]

f(x), when you replace x with a number, which is 0, you’re asking; what value is y, when x is 0?
It’s basically the same as the limit question, but not rlly. anyways look at x = 0

There is only one line that touches the y axis, where x is 0

Hint: it’s from before

[forest epoch]

-5?

[uneven rapids]

Yes

Ur getting it

[forest epoch]

for this one**,** would I do the same thing or**...** no**?**

[uneven rapids]

Firstly can you mark x = 3?

[uneven rapids]

Ok now create a vertical line (top to bottom) at x = 3

And tell me y value that little open circle at x = 3 equals to

[uneven rapids]

Now look at the y-axis, what value is the open circle?

[forest epoch]

3**.**

[uneven rapids]

It’s negative 3 since (-) means negative

And on the y axis, anything lower than 0 is negative

Y axis is top to bottom

[forest epoch]

oh**.**

i've read it wrong**..**

😅

[uneven rapids]

Before solving the limit question, look at the line at -3, does it act the same?

Like I’m saying, does the “line” or function behave the same when it’s near x = 3, the right and left side?

[forest epoch]

uhm**..**

im not sure**..**

[uneven rapids]

From the right side, you can try putting your finger on the line and following it until it reaches x = -3

Do it with the left, and tell me did your finger go in the same direction from both sides?

[forest epoch]

y**-yes..**

[uneven rapids]

Then tell me, does the limit exist or not?

Given what ive previously said about limits existing

[forest epoch]

y**-yes..** it does exist**...**

[uneven rapids]

That’s right, and since it does exist, the answer for all 4 should be the same

limit: x -> 3 from the right side, what is the y value?
We did this earlier, and it’s -3

And since the right side = left side here, that means it’s -3 from the left side too, which means the limit also does exist, and f(3) is -3

Are you starting to understand it more?

[uneven rapids]

Here

[forest epoch]

a little bit**..**

[uneven rapids]

Tell me when you’re on the next problem

[uneven rapids]

The first 3 questions are the same answer,

Since the limit does exist, you don’t need to put DNE

[uneven rapids]

Try to do this one on your own, when you think you’re finished send me all your answers and I’ll check it

This one is like the previous one

[forest epoch]

do I do the same thing**?**

[uneven rapids]

Yes it’s the same thing like the other one, but different numbers

[forest epoch]

would f (2) = 2**?**

[uneven rapids]

Yes

What are the other ones now?

[forest epoch]

is it -2?

[uneven rapids]

For which one? All of them?

[forest epoch]

the 1st one**..**

[uneven rapids]

It’s just 2, when x = 2, the y value is 2, it’s not -2 (as you can see by the line)

[forest epoch]

so far**,** I have my 1st and last answer as 2 .

[uneven rapids]

Ok now observe the line from the positive side, once you reach x = 2, what value is ur finger point to, on the y axis? Is it the same? is it different?

[forest epoch]

wdym by that**?**

is it from the x-axis ?

[uneven rapids]

Move your finger across the line, but when you reach x = 2 (X AXIS), you look at the y axis

What y axis value do you get

[forest epoch]

2**.**

[uneven rapids]

That’s right

And since the left side and right side is the same, the function indeed exists

When the function exists, the limit is the same as the ones you got previously (whether it’s right or left side), they’re both the same anyways.

[forest epoch]

would this be correct ?

[uneven rapids]

Yes now the other one is 2

[forest epoch]

i got it wrong

the last answer of f (2) is Undefined

[uneven rapids]

Oops I forgot to mention that an open circle means either less or greater than

So yes it’ll be undefined at that specific point

It’s almost 12am sorry

Open Circle: less or greater than
Closed Circle: less, greater than, OR equal to

[forest epoch]

its ok**..**

[uneven rapids]

• When a function approaches the same y value from both the right and left, then the limit is defined. Given this, the limit for left & right side will be equal.
• When a limit approaches 2 different y values at a given x value, the limit does not exist (DNE)
• Open Circles: either less or greater than, cannot be equal to.
• Closed Circles: less, greater, and is able to be equal to.
• Left side (negative x values)
• Right side (positive x values)
• Y Axis (Horizontal: top to bottom)
• X Axis (Vertical: right to left)

This is basically all the rules so far

I don’t think you know what continuity is yet, correct?

@forest epoch

[forest epoch]

n**-no..**

[uneven rapids]

Okay you don’t have to worry about it until your school teaches you it, but continuity is how continuous a function is

A discontinuity means a breakage in continuity in the function

@forest epoch any more problems?

[forest epoch]

well**..**

its almost 12am for me ..

[uneven rapids]

So you’re leaving?

It’s almost 12am for me too

[forest epoch]

y**-yes..**

i need to go to sleep**..**

i dont want to stay up**..**

[uneven rapids]

Okay goodnight if you learn anything new at school I can help you with it

[forest epoch]

ok**.**

I**'ll probably work on this math problem tomorrow.**

If I have any questions**,** I**'ll ask for help..**

[uneven rapids]

This one is a different and harder than the other ones

So yea that’s fine

Bye

[forest epoch]

bye Rel !

[uneven rapids]

Nevermind just analyzed the problem it’s essentially the same

Ok ok bye now have a great night

[forest epoch]

you too**,** Rel !

[uneven rapids]

I