Figure It Out
P.R.O.B.L.E.M.S Lyrics

Jump to: Overall Meaning ↴ Line by Line Meaning ↴

In this sea of emotions I'm floating
Ain't no shore
That's for sure
Looking out my window, new views
They always change
They never stay the same
I just need some clarity
Will you hold my hand

Transitioning into a man
I don't have a thing figured out right now
Yea
My mind is full of doubts
Soon
It'll all be figured out
You can rest your head
It'll all be said and done in the end
Think of the best case
Life sure ain't a race
So baby slow it down we'll figure it out
Out
Yea
Nah nah nah nah nah
In the end
Soon
It'll all be figured out
You can rest your head
It'll all be said and done in the end
Think of the best case
Life sure ain't a race

So baby slow it down we'll figure it out
Out

Overall Meaning

The lyrics of P.R.O.B.L.E.M.S's song Figure It Out explore the internal conflict of a character who is deciding whether to continue investing in a relationship or to give up and move on. The opening lines depict a sense of confusion and chaos as the character is running away from both the person they are in a relationship with and their own thoughts. The question posed in the lyrics "Can you believe in us? Worth fighting?" signals that the character is unsure if the relationship is worth fighting for, indicating a lack of clarity and certainty.

The following lines of the song delve deeper into the character's psyche as they grapple with their personal issues that could potentially affect the relationship. The lines, "By ourselves, wanting to be more," suggest that the character believes that they are insufficient on their own and that they need someone to help them be better. The repetition in the next few lines, "You can skip to the end/And then have time for yourself/If that is fine for you/Can't answer to yourself" indicate an indecisiveness that the character may be struggling with, as they cannot seem to settle on what they want. The concluding verses of the song suggest that the character is seeking clarity and trying to come to a decision on the relationship - "tell me something that you think it's worth it/ So we can figure it out", which is repeated as the refrain of the song.

Line by Line Meaning

I've been running away from you for hours
I have been avoiding you for a long time

I've been running away from myself
I have been avoiding facing my own issues

Can you believe in us? Worth fighting?
Do you think we have a chance together and is it worth fighting for?

By ourselves, wanting to be more
We are both individually striving to be better

With me is the only time she could be worth it
She only sees her own worth when she is with me

I don't know how I can get it, figure it out!
I don't know how to make this work, I need to figure it out

Tell me something that you think it's wort it
Share with me something that you believe is worth pursuing

(Worth for me) So we can figure it out
Let's work together to figure out what is worth it for both of us

The more you treat me, I adore you
The more you show me love, the more I appreciate you

That's why I remind when these things for you
That's why I remind you of the good things you do for me

When I wedged the doors, I caught you on a Wednesday
I caught you in the act of doing something wrong

Mr. Tl on the phone, fuck what your friends say
I don't care what your friends say, I trust Mr. Tl

It's too dumb, it's trending, tell me, if you hear me
I don't want to follow what's popular, tell me if you understand

Lord, fuck the faith, give up any boredom
I don't care about religion, let's live life without being bored

I fucked up, it's hard
I made a mistake and it's difficult to fix

Lyrics © DistroKid
Written by: Matthew Andrawis

Lyrics Licensed & Provided by LyricFind

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Comments from YouTube:

@bprpcalculusbasics

17w↑82

Why doesn’t this limit represent the definition of derivative? 👉https://youtu.be/C440uWSzFGg?si=Zx-wuAEkbfV5_m8a

@BlacksmithTWD

16w

This immediately reminded me to when I was thought the limit of 1/x as x goes to 0 to illustrate why one can't divide by 0.

@user-bd1tk1yr1w

16w↑1

but if we use L Hospital rule and differentiate the numerator and denominator then we have 1/1-0 which equals 1 so by that method the limit should exist and should be equal to one

@BlacksmithTWD

16w

@@user-bd1tk1yr1w Not familiar with the L Hospital rule, So I wonder how you got from x/(x-1) to 1/(1-0) or 1/1-0.

@mondherbouazizi4433

16w↑2

@@user-bd1tk1yr1w We can only apply the L'Hospital's rule if the direct substitution returns an indeterminate form, that means 0/0 or ±∞/±∞.
As bprp said, this is NOT an undeterminate form. The limit is clearly ∞, but depending on the direction from which we approach 1, the sign of ∞ changes

@om-qz7kp

15w

Brilliant. I like this kind of videos. Subscribed🎉

4 More Replies...

@HalobeatWatcher

17w↑3.1K

Honestly I think the class didn’t learn limit from right and left or they just forget about it.

@Lordmewtwo151

17w↑40

Well, in both cases the function approaches 1/0. However, where x is less than 1 and greater than 0, the function is negative. Likewise, when x is greater than 1 or less than 0 (which is irrelevant to this question), the function is positive.

@JasperJanssen

17w↑37

I did learn about that (albeit 25 years ago, oh god, and not with this guy’s notation) and my first reaction was that it doesn’t specify from which side it is in the problem.

@thetaomegatheta

17w↑47

@@JasperJanssen
Why is that a problem? If the side is not specified, it's obviously the standard, and not a one-sided limit.

@JasperJanssen

17w↑7

@@thetaomegatheta … did you watch the video? And no, there is no such thing as “the standard”.

@thetaomegatheta

17w↑36

@@JasperJanssen
' … did you watch the video?'
Yes, I did.

'And no, there is no such thing as “the standard”
Do you seriously not know about the non-one-sided limits?

38 More Replies...

@henrikholst7490

16w↑913

Note to self:
"L'Hôpital's rule can only be applied in the case where direct substitution yields an indeterminate form, meaning 0/0 or ±∞/±∞. So if f and g are defined, L'Hôpital would be applicable only if the value of both f and g is 0. "

@homebird4765

15w↑50

I made the same mistake

@vedantlearns7516

15w↑18

same mistake here😢

@Sanji-ip1vd

15w↑18

Same and got answer one

@vintovkasnipera

15w↑6

If it's a school or university question, L'Hôpital's rule shouldn't be accepted as a valid proof to be honest

@homebird4765

15w↑21

@@vintovkasnipera Why's that?

9 More Replies...

@wtmayhew

17w↑1.1K

This limit problem is a good illustration of why making even a rough sketch graph of the function in question can shed a lot of light. Using a graphing as a qualitative analytical tool is too often overlooked.

@levaniandgiorgi2358

17w↑19

While i do agree that graphs are amazingly helpful,i believe more complex problems would be better suited for them,idk.. to me, the answer felt glaringly obvious from the start.

@wtmayhew

17w

@@levaniandgiorgi2358 I largely agree. I looked at the statement and pretty much saw the answer immediately, but then I have the advantage over freshman students of having done math for close to 60 years. I’ve encouraged students to not shy away from sketching Bode plots or pole/zero diagrams in the EE courses I’ve taught. It is handy to look at a problem with more than one method to avoid mistakes. The backup method doesn’t need to be precise, just accurate enough to confirm your thinking is on track.

@ivanzonic

17w↑14

No reason to waste time graphing something like this

@heylolp9

17w↑33

Graphs do what Graphs are supposed to do, give you a visual representation of the abstract equation

It's helpful for people who are stronger visual learners to link the reasoning and the answer together

@sankang9425

17w↑14

Graphs are very powerful. It's really hard to believe calculus was invented without using them. People make fun of 'trivial' stuff like rolle's theorem, but good luck proving them without graphs.

12 More Replies...

@joaooliveirarocha

14w↑138

I just woke up and this video was suggested. I haven't touched in limits for almost a decade so my thought was "Ive forgetten all of this".
I've opened the video,watched for 3 minutes and I could feel the knowledge coming back 😂 so weird

@dscarmo

Thats how most people say videos are teaching more than school

In reality its just bringing stuff back.

@cvkline

16w↑55

Cady Heron would have figured this out… it’s how she won the athlete competition in “Mean Girls.”

@StaticBlaster

16w↑5

I love the movie reference.

@contextinvideos

17w↑463

never took a calculus class in my life but i still end up watching these videos

@jamescollier3

17w↑8

took multiple calc DQ and didn't really like it, but watch

@muneebmuhamed43

17w↑8

studying in class 10 but still watched cuz why not 😂

@jim2376

17w↑4

Admirable curiousity. 👍

@dominicj7977

17w↑4

@@jamescollier3 I never really liked math as a whole in college. Then once I graduated, I started learning it in depth, on my own . Then I started loving it.

Now it has been 7 years since I graduated and I still learn it

@operator8014

17w↑5

My calc class explained SOOOO MANY of the questions I had about things that didn't make sense from earlier classes. Can recommend.

4 More Replies...

@Stags28

17w↑180

I used to love asking my students on these if their denominator was positive zero or negative zero. The transition from initial confusion to a-ha was one of my favorite gems from teaching.

@krishnannarayanan8819

17w↑8

Sorry, I don't understand what positive and negative zero mean. Could you please explain?

@BlueGamingRage

17w

@@krishnannarayanan8819shorthand for "approaches zero from the positive direction" and negative directing, respectively

@l.w.paradis2108

17w↑22

@@krishnannarayanan8819 A shorthand way of saying to approach 0 from x < 0, or x > 0.

@Keneo1

16w↑2

@@krishnannarayanan8819it means 0 or -0

@morijin5568

16w

@@krishnannarayanan8819 you could assume some number "h" which is a very small positive number. positive 0 means 0+h and negative 0 means 0-h . basically 0+ and 0- are approaching 0 from right and left sides respectively.

2 More Replies...

@houghwhite411

17w↑14

I haven't been to school for at least 5 years, and now listening to your explanation I could understand better what I could not back then

@bobtivnan

17w↑61

Knowing how this function's graph behaves gives all of the intuition needed. Vertical asymptote at x=1, positive to the right, negative between 0 and 1. My students often dive into the calculus without thinking about the precalculus. Sure it can be done without the precalc, but the confidence gets a big boost when we think about the graph first.

@No-cg9kj

17w↑2

And that's how you get 0 points for the question on an exam. You're expected to do the calculus on a calculus exam.

@bobtivnan

17w↑16

@@No-cg9kj read more carefully

@bramvanduijn8086

17w↑3

Approaching a limit doesn't require a Y-axis, you're needlessly complicating the concept and conditioning them with a euclidian bias in their thinking about numbers.

@iamcoolkinda

17w↑8

@No-cg9kj On any calculus exam, this question would be a multiple-choice or short answer question where you’re either right or wrong, no partial credit. Graphing is sometimes way faster than doing the math. just visualizing the graph i solved this problem in probably 2-3 seconds

@thetaomegatheta

17w↑3

@@iamcoolkinda
'On any calculus exam, this question would be a multiple-choice or short answer question where you’re either right or wrong, no partial credit'
Literally none of the math exams that I took at university had multiple-choice questions. You needed to actually demonstrate your knowledge of the topic, and, in the case of specific problems like that one, you had to present solutions.

1 More Replies...

@cmyk8964

17w↑139

Finally! A problem on this channel I could solve on my own!

@RavenMobile

17w↑7

This channel is way out of my league 99% of the concepts he deals with... but I still come back to watch more, lol. I like how he explains things and how he writes on his whiteboard.

@bananatassium7009

17w↑2

brilliant explanation, these videos really make me feel like I'm getting a better grasp on calculus as someone who's never taken it but is passionate about math :)

@johnelectric933

17w↑7

Thank you. The limit pops up a lot in engineering, not just on paper but in actual physical or electrical functions.
That said, in electronics we use graph paper as writing paper so doing a graph with 3 samples is quicker.

@its_elkku135

17w↑110

I love this bite sized math content, feels like I'm getting a bit smarter every day :D

@ravenousstrike012

17w↑12

I just literally advance self-studying Calculus 1 rn and this is my 1st video yt recommend it. I didn't know that we can also have exponential signs to determine if + or - infinity but i alr knew that it will be DNE bcuz of + & - infinity are not equal. Perfect timing! I can't wait for my next sem. You got a sub❤!

@bprpcalculusbasics

17w↑2

Glad to hear! Thank you!

@benrex7775

12w↑1

It's been a while since I did this type of stuff. Thanks for the refresher.

@frostshock13

17w↑8

I haven't taken calculus in my life and was interested. Only to be completely distracted by the lifetime supply of expo markers.

@jorwinwithcoffee

17w↑12

Merry Christmas Bprp 🎉

@bprpcalculusbasics

17w↑6

Thank you! You too!

@Lolwutdesu9000

17w↑13

Are we not gonna talk about the amount of markers he's got stored in the background? I've seen entire schools have less than that lmao

@user-zo1kn8ob7h

15w↑2

your teaching style is comforting
i still dont understand this one due to my lack of foundational knowledge, i think.
still very glad to have your vids

@_Just_Another_Guy

17w↑118

Btw, the graph shows that the two lines doesn't meet at a certain point (diverging on an asymptote) so that's what DNE literally means: there's no convergence at any particular point.

@bartiii7617

17w↑44

DNE actually means "does not exist" lol, a limit can still exist even if theres no convergence at any particular point, e.g. diverging to positive infinity/ negative infinity

@bartiii7617

17w↑11

maybe its TNCAAPP: "theres no covergence at any point"

@hyperpsych6483

17w↑22

@@bartiii7617 limits diverging to positive or negative infinity also do not exist by the delta epsilon definition, though most people just go with the "you know what i mean" equals sign

@hydroarx

17w

@@hyperpsych6483can't you use the epsilon-N/delta-M/N-M definitions for those limits?

@alexatg1820

17w↑4

@@hyperpsych6483I think it depends on the topology we’re working on, tho in common topology of ℝ we regard ±∞ as DNE, so I agree with you

24 More Replies...

@nirorit

17w↑8

I personally prefer using two sequences to show that. X_n=1+-1/n, and then the functions turns to to 1+-n, and when you take its limit you get +-infinity.
Feels more rigorous to me.

@Umbra451

17w↑37

Nice video! It’s been a while since I’ve done this. Since we did indeed get the conclusion that we would expect from inspection, could you give an example of a limit that looks DNE at a glance, but turns out not to be?

@literallyjustayoutubecomme1591

17w↑9

Well, that depends on how good your glances are, doesn’t it :)

@Steve_Stowers

17w↑3

@@literallyjustayoutubecomme1591 Agree. To beginning Calculus students, a limit often "looks DNE" as soon as they see that 0 in the denominator (even if the numerator also approaches 0).

@jackbrax7808

17w↑2

As someone else stated, it sort of depends on how good your “glance.” Is. If your very proficient with limits and calculus, you potentially could have know just by looking at the limit what the answer would be.

But a great example in this case would be x/(x-1)^2. Having a square term in the denominator actually causes the limit to approach positive infinity from both the left AND the right. Therefore the limit actually approach’s infinity and therefore does exist!

@Steve_Stowers

17w↑2

@@jackbrax7808 Depends on what you mean by "exist." According to most basic Calculus books I'm familiar with, if the limit is ∞, the limit doesn't exist—you're just being more specific about how/why it doesn't exist.

@jackbrax7808

17w↑2

@@Steve_Stowers I just double checked my definitions and turns out your right. It doesn’t exist but both sides tend to infinity. But due to infinity not being a number, it doesn’t exist. But you can say the limit tends to infinity.

3 More Replies...

@edrodriguez5116

17w↑1

Merry Christmas Mr. bprp!

@maburwanemokoena7117

15w

I once drew a piecewise function for my learners, below 2 it was defined as x and from 2 and above it was defined as x+2, I asked them to determine the limit of the function as it approaches 2. I realized they had long forgotten about approaching a point from the left and right, they've gotten used to simplifying then "substituting" the limit value.

@mehulgamer2836

17w↑17

I was not getting LHL = RHL so I knew the limit does not exist. Btw Merry Christmas bprp :D

@jmz_50

17w↑4

Good video as always

@derekyu4430

12w

in my opinion, this question is the best way to tell us why concepts are important.

@somebodyxd9837

13w

took me like 3 seconds but my lack of trust in myself and curiosity kept me here lol

@matthewlloyd3255

17w↑6

Almost all limits can be evaluated by doing a thought experiment of "what happens if I move just ever so slightly to the left/right/both sides of it" - and then playing it out in your head.

@glumbortango7182

17w↑9

This question gets a bit easier if you rewrite x/(x-1) as (x-1+1)/(x-1), which is 1 - 1/(x-1), which is a little more obvious in how it behaves as x -> 1. Fairly simple explanation though.

@RedGallardo

17w

The right usage of infinity is a gulp of fresh air.

@user-qp2wi6yj4d

15w

I honestly think that people usually forget, checking the limits right and left to just verify that the limit exist, usually what they do and what I did initially is I added one and subtracted one from the numerator and some split it in kind that it becomes one plus one by X minus one extends to one. So the whole thing tends to infinity which tends to zero so overall the limit would have been one but that points out to be incorrect.

@welcometotheshow5247

17w↑7

I always loved problems like this, it always reminded me that when u set up a number line the distance btw what ever numbers you end up choosing is infinite and if you wanted to count every number btw that distance you would always be approaching a certain number and never really reaching it.

@naveen-bu7du

15w

Thankyou for revision 😀

@electrodynamicorb6548

17w

It’s been 16 years since I’ve taken any calculus but knew right away it was undefined or does not exist

@theknightikins9397

17w↑3

While I do like the idea of the plus on the zero meaning a number arbitrarily close to zero, for problems like this I always think of it a “positive” zero. It’s functionally the same and gets the same answer, I just find it easier to understand, if you divide a positive by a positive, you get a positive. Is the zero positive or negative, not really, but if anyone is having trouble understanding this, try thinking of it this way.

@fioscotm

17w↑1

Huh, that actually is a really nice way of thinking of it. Thanks for this!

@tomekk.1889

17w

It might help you with limits but it's not functionally the same. It's worth learning what 0+ actually means and sticking to that it will help you later with series etc

@andrewparker8636

17w↑13

I personally think it's easier to approach these problems by changing the limiting value to 0. That way it's obvious what's +ve and -ve. In this case, we could change the limit to lim e->0 (1 + e) / e by substituting x for 1 + e (e is supposed to be epsilon here). Then you can work out lim e->+0 and e->-0 and it's a little easier (IMO).

@nicolastorres147

17w↑1

Converges in the one point compactification of the reals 🤯

@first-namelast-name

You can also answer lim_x→1[x/(x-1)]=∞ without precising the sign, and it means that there is an asymptote at x=1 in this case, without telling from where the function approaches it. Be careful not to mistake it for lim=+∞, tho, this one would mean that the limit is defined.
This is also why I would recommend to always say +∞ instead of just ∞ when the value is positive.

@Zzzzzzzzzzzzzn

17w↑3

From the times, when I was a student, I remember three different intinities: "+∞", "-∞" and "∞". So we explicitly used sign, if the infinity had one, and not used if that was "just the infinity", when sign is unknown (or does not matter). Is this the case nowadays? You are never using "+∞" notation, always omitting "+" sign...

@Mr.Not_Sure

17w

Same

@thetaomegatheta

17w↑1

The space that is assumed in the video is the standard extension of R with two points at infinity - +∞ and -∞. Unsigned ∞ does not exist in that space.
I think it's a bad decision on the author's part to not explicitly state what space we are looking for a limit in, as in other extensions of R that limit does exist.

@userchrh

17w↑17

I've found another method. We know that x/(x - 1) = ( (x - 1) + 1 )/(x - 1) = 1 + 1/(x - 1). So the limit equals 1 + lim_(x -> 1) { 1/(x - 1) }, or just 1 + lim_(x -> 0) { 1/x } which we know DNE.

@colinjava8447

17w

When I took a course on it, lecturer said it doesn't exist (rather than its infinity), but on the video he's calling it infinity and -infinity, and for that reason the limit doesn't exist.
I think I prefer saying it doesn't exist, but saying its infinity or -infinity gives you more insight into the shape of the graph I guess.

@janskala22

17w↑2

@@colinjava8447 The limit exists if and only if the right limit equals the left limit. If left limit is different from right limit (in a given point), the limit does not exist. The limit is not "either inf or -inf", it just "does not exist".

@colinjava8447

17w

@@janskala22 I know, that's how I knew in 2 seconds that it doesn't exist (cause left =/= right).
My point was in the video he writes infinity, when like you said it just doesn't exist.
I think he knows that probably but does it for convenience.

@janskala22

17w↑2

@@colinjava8447 He only writes infinity on the right limit when it holds. He writes -infinity on the left limit where it holds. He does not write any definitive answer to the whole limit until he is sure it's DNE.

@colinjava8447

17w

@@janskala22 I know, I saw the video too.

2 More Replies...

@user-iy4bt6gv7p

17w

this is called sidded limits, when we know that theri is a discontinuity but the plot has one side going up and the other going down.
The plot makes it easier to understand.

@guerrillaradio9953

17w

Unless you consider using the Riemann Sphere (extended complex plane). The only problems with it are when attempting to divide zero itself by zero, but we aren't trying to do that here, so the identity checks for all numerators not equal to 0.

@r75shell

17w↑4

Do you think a teacher or other person who check your work will be fine with 1+/0+ argumentation?
I think better would be substitute y = (x - 1) so, we need to calc (y + 1) / y with y -> 0
then (y + 1)/y = 1 + 1/y, thus for y > 0 it (y + 1) / y > 1 / y, but 1/y -> infinity
but for y < 0 it doesn't work. so I think just use some fact lim (x + C) = C + lim (x). idk.

@dielaughing73

17w

It's how I was taught at uni. Best to check with your professor if you want to be sure.

Don't forget you can always (and often should) add annotations in plain language explaining what you're doing and why. Then it doesn't really matter what notation you use, as long as it's clearly defined and consistently applied.

@AryanRaj-fz7dd

17w

@@dielaughing73 our professor also uses these notations what the hell is wrong with it

@billmilligan7272

17w

This is how I was taught as well. If a teacher or other person who will check your work isn't fine with it, it's time to talk to their boss.

@kazedcat

17w↑2

Just replace 1+ with 1+ε and 1- with 1-ε.

@anonymousf7byyj

17w

@@billmilligan7272thanks for your input Karen

2 More Replies...

@darcash1738

17w↑4

Nice, this is exactly how I did it. Can you post more proofs for common derivatives using the limit definition of (f(x+h) - f(x))/h? I think it could be fun to do a whole series on that. I tried the polynomial one for myself, and was able to confirm that (x^n)’, using binomial theorem and being left with just the second term was nx^(n-1). I tried getting the derivative of e^x = e^x, but I couldn’t pull it off tho, wasn’t sure how to bring out the h 😂

@Syndicalism

15w

exp(x) is factored out of the limit. The remaining limit is [exp(h)-1]/h which evaluates to 1.

@darcash1738

15w

@@Syndicalism nice! I looked at the standard way I guess you could call it for evaluating the last part, where you say that some variable, eg k = the top part, so it becomes k->0 k/ln(k+1). Bringing the k up top to the bottom w reciprocal, and then log power rule it becomes 1/ln(e) = 1.

The main part that was sort of unexpected for me was the start, setting the top to a variable. How might we stumble upon this—just trying it out bc it’s limit approaches 0 as well? Also do you think that mathematicians found out the derivatives first and then tasked themselves with proving them?

@sshep7119

17w↑1

-X approaches a vertical asymptope from the left, whereas +X approaches a vertical asymptope from the right. If -X doesn't equal +X the limit does not exist.

@michaelm1

17w↑2

This is incredible. I cannot believe it. This has got to be some kind of a record. A miracle. I tried it and I got it right. I never get things right. This got to be the exception to prove the rule. Wait...

@bDe4d

17w↑5

Man, my teacher has been hammering our class wuth this for months and bearly anyone understood even the priniples of "limit" and how you check for it.
I'm just now trying to keep up with the material as we're quite past that and even had a small test (which I failed, miserably) and I'm going to definitely retake it soon as thanks to you I understand everything perfectly, even though English is not my first language haha

Lots of love from Poland! Cheers!

@thetaomegatheta

17w

'Man, my teacher has been hammering our class wuth this for months and bearly anyone understood even the priniples of "limit" and how you check for it'
Let me guess, your teacher said that a limit is something that a function gets closer and closer to as its argument gets closer to some point?
Yeah, I'd advice looking up an actual definition of a limit.

@clmasse

17w↑4

It's normal, there is no limit. Ask the good question: what is the + or the - limit? The problem is often the nut behind the whiteboard.

@marvinliraDE

17w

If you have a function 'f' which is defined on a subset 'M' of real numbers and you have some real number 'y', then the left-side limit 'lim_{x->y-} f(x)' is defined as the limit 'lim_{x->y} g(x)' where 'g' is the same as 'f' but restricted to the subset of 'M' containing only the numbers that are at most 'y'. The right-side limit is defined analogous.

@marvinliraDE

17w

So visually speaking, you cut your function at the point 'y' into a left side and a right side and handle each side on its own.

@OnurOzalp-personal

17w

how did u know i nut behind the whiteboard? also he answered those as + and - infinity already.

@clmasse

17w↑2

@@marvinliraDEThe point is, the limit of the function defined on ℝ\{1} doesn't exist. The problem is in the question (asking for something that doesn't exist,) not in the answer, for DNE is not the limit of the function.

@dielaughing73

17w↑1

@@clmasse I'm not sure there's anything wrong with asking a mathematical question for which there is no defined answer.

Would you feel better if the question was "what is the limit of <function> as x approaches <value>, if such limit exists"? Because I'd think the qualification is implied for students beyond the most rudimentary level of maths.

1 More Replies...

@BigDBrian

17w↑1

Got it correctly! Remembering stuff from years ago that I learned from bprp

@StAngerNo1

14w

I don't know why this video got recommended to me. I would not have know the correct notation, but figuring out the answer is quite simple.

@bprpcalculusbasics

17w↑21

Is this a well-defined limit? Calculus question on Reddit r/askmath
https://youtu.be/WaFEqnPGzCo

@colinjava8447

17w↑5

I guessed that it was undefined in 2 seconds, cause its essentially 1/x, and its a limit from both sides.

@dominicj7977

17w

hi, an easier way is to substitute x-1=t

so the limit is t-> 0 for {(t+1)/t }
which is equal to t-> 0 for {1+1/t }

@adrified9352

17w↑5

DNE since f has a VA at x = 1 and f is odd

@epikherolol8189

17w↑2

Vertical asymptote?

@thetaomegatheta

17w

If we just assume the standard extension of R with two points at infinity, then yes.
If we don't, there is another fairly standard space where the limit does exist - the standard extension of R with one point at infinity.

@uberless1

17w↑8

I am absolutely certain that my Calculus teacher from 20ish years ago would have hated your 0+ notation…. She wanted derivative tests all the way.

EDIT: To clarify, she would obviously have been fine with 0+ in the initial limit, but she wouldn't have liked 0+ as a result of partial computation. [Though it does seem intuitive as shown in this video.] She would have considered this an "invalid shortcut".

@tomctutor

17w↑4

f' (x) := lim (h->0) (f(x+h) - f(x))/h
well that's how I was taught how to find the derivative, using First Principles as it were.
However when they teach Calc1 now they miss out this and expect you to look the derivative up in a table, usually supplied with the exam, whats the point of even learning calc this way! 😟

@bernhardbauer5301

17w

1/0 is not allowed.
1+ and 1- are not numbers.
1/x has a singularity at x=0.
This singularity is shifted in his example.

@shawnmiller4781

10w↑1

I think I found my problem with high school math.

Getting distracted.

Such I was by this video by that impressive ready to go supply of dry erase markers in the lower right hand of the screen

@arandomperson8336

17w↑1

I graphed it and it approaches negative infinity from the left and positive infinity from the right so if I remember my calculus correctly that means the limit doesn't exist, although the one-sided limits do. Now I will watch the video and see if my 2-second-effort-because-I'm-not-in-college-anymore answer is correct...

Yay I got the right answer on a math video for once!

@melonenlord2723

17w↑4

Of course class couldn't figure it out if no solution exists 😂

@isaacbruner65

17w↑3

There is a solution and the solution is that the limit does not exist.

@omp199

17w

@@isaacbruner65 To say that the limit does not exist is just another way of saying that there is no solution to the problem of finding the limit. The statement that a solution does not exist is not in itself a solution. If it were, then you could say that every equation has a solution, which makes a nonsense of the concept of a solution.

@kazedcat

17w

@@omp199it's different with limits. "The limit does not exist" is part of the set of possible solution with limits. Similar to NaN is a possible answer to a floating point operation even though NaN literally means Not a Number.

@omp199

17w

@@kazedcat No. It's not "different with limits". A solution is a value or set of values that satisfy a given set of conditions. If the condition is that of being the limit of an expression, then the nonexistence of a limit implies the nonexistence of a solution.

As for "Nan", you are bringing programming language conventions into a discussion of mathematics. A programming language might have a function that returns NaN in certain circumstances, but that has nothing to do with mathematics.

@kazedcat

17w

@@omp199 Programming is mathematics. The Turing Machine is a mathematical object.

1 More Replies...

@Harishkumarindianrailways

17w↑307

Why L hopital rule is not used here

@OK-ei7io

17w↑496

We don’t have an indeterminate form.

@YourNeighbourJack

17w↑516

Because L’hôpital rule only works with 0/0 or infinity/infinity

@Harishkumarindianrailways

17w↑57

Understood

@teelo12000

17w↑585

Because the injury isn't bad enough to go to L'Hospital.

@J-M784

17w↑25

@@teelo12000 This isn’t ‘la Páris’! 😂😂😂😂😂😂😂😂😂😂😂😂

23 More Replies...

@huzzzzzzahh

17w

Out of the corner of my eye I thought this was loss

@OverlordSpirit

15w↑1

How the hell his whole class wasnt able to solve it, it's literally the basic LHL=RHL

@lucaspanto9650

17w↑3

Looks like it just tends to ∞

@isaacbruner65

17w

That would imply that it tends to positive infinity which is obviously not the case.

@lucaspanto9650

17w↑2

@@isaacbruner65 🤓

@thetaomegatheta

17w

@@isaacbruner65
No, it would not.
There are multiple extensions of R, one of which is assumed by BPRP in the video and has two points at infinity, and another one has only one point at infinity, which we can call 'unsigned infinity' for clarity's sake. In the case of the latter one, the person you responded to is absolutely correct, and it is a bad thing that BPRP did not explicitly bring up the matter of the space in which we are supposed to look for a limit.

@aarusharya5658

17w

@@lucaspanto9650 Your dumbass said the limit tends to infinity. I doubt you're in a position to use that emoji.

@epikherolol8189

17w↑4

I figured out it DNE in 5s lol

@General12th

17w↑15

Do you want a sticker?

@Sukunut

17w

@@General12th lol

@shortsimple1847

13w

My Teacher in the L1 of Limits told me about the 8 indeterminable forms: 0/0, inf/inf, inf - inf, 0^0, inf^0, inf*0, 1^inf. Anything except these including 1/0 [inf] is defined {though the limit may not exist}.

@pinnaclerigde3056

17w

it is ±infinite depends on which side you take.
- if approach from -inf to 1
+ if approach inf to 1.
You can easily check using scientific calculator. Type in the function and calculate wiith x= n±10^(-6)

@thetaomegatheta

17w↑1

'it is ±infinite depends on which side you take'
lim(x/(x-1)) as x->1 considers points in the entire neighbourhood of 1. You are thinking of one-sided limits.

@slickysaturn7243

@bprp ir i have a very stupid doubt, for x≠1 is this function continuous throughout its domain. My math textbook says yes but i need to the understand the logic.

@setsunaes

16w↑1

Wow, I still remember calculus!

@prachiagarwal5674

Thank you so much for this helpful video! I am wondering why did we not use the L'Hopital rule? In high school we were taught to use it to solve limits where the denom == 0

@Yupppi

Is there no fancy way like multiplying with x+1 or the usual trickery for limits I never really learned well enough to understand?

@joyneelrocks

You can use graphical methods too: x = x - 1 + 1 ==> x/(x - 1) = 1 + 1/(x - 1). So y = x/(x - 1) is basically the 1/x graph shifted to right by 1 and up by 1 unit. As x —> 1, x/(x - 1) diverges. So limit does not exist if you know the 1/x graph well.

@flstep835

15w

damn left and right limits really got me on this one

@oliveiraoliveira9281

17w↑2

Hi,
Do you have any vídeo which you have found the critical points, created the chart, founded the maximum and the minimum??

All in one process...

@SuryaBudimansyah

17w↑1

I remember he has a video about function increasing/decreasing, concave up/down, and point of inflection, not long ago

@tomctutor

17w↑2

Optimization usually learnt in high school maths, with or without a bounded domain you should always use calc.
I assume you mean the Nature Table method when you say 'chart'
The exception (where you do not need calculus) would be quadratic relation as the vertex gives you the optimal value (using complete the square).

I agree a video on Optimization (with bounded intervals) using Calc would be most welcome. 🤔📈

@oliveiraoliveira9281

17w↑2

Hi @@tomctutor thank you by answer. By chart I mean to put the curve over the axis "x" and "y".
And yes you are right, using the nature table method....

@The_Senorita-In-the_Dream

17w

This is fucing essential

@fromthegamethrone

13w

And here is me, still accidentally opening calender instead of calculator on my phone 😢

@GoatTheGoat

17w

At 5:43 the denominator should be written as -0(plus). It is a negative number, with a magnitude just larger than zero.

@kaikulimu

17w↑1

Good old math yay! I simply said "negative infinity" since I only considered x approaching 1 as x = 0.99999999, but yeah it could have been x = 1.000000001 too.

@Emily-fm7pt

16w

I tried to substitute u=x-1 so I could get a simpler (in my head) expression of lim_u->0[(u+1)/u] = lim_u->0[u^-1 + 1], which I just know the graph of and can see that it's indeterminate

@swalbi1579

17w

I always imagine coming from the left and right to approach the number in such cases (also I make gestures with my fingers 👉🏻👈🏻😂)

@chucksucks8640

17w

I could only figure this out if I drew the graph and realized that the positive and negative directions gave different answers. But I think I would have gotten this test question wrong because I would have just used simple substitution and came up with positive infinti.

@pushkarroy9740

17w

meanwhile me applying componendo and dividendo and getting 1 as answer

@jeff5101

17w

Glad you weren't one of my engineering professors

@PradhithPothuri

14w

That is an amazing explanation!
But you always can't do a process this long in the examination.
There is a simple trick.
To find if a limit exists for a given function , first substitute the limit in the function.
If the result is a real number, well and good. But if it is not check whether the result is in the form of 0/0 (or) 0/any real number. In this case the limit exists. If the result is in the form of any real number/0 , the limit does not exist.

@anipurasu

17w

OMG! What should I watch, your T-shirt or the math 😆

@leo-um3pj

17w

i just immediately draw the graph in my head then boom dne

@angelmatematico45

10w↑1

If the limit tends to infinity, it does not exist, because infinity is a concept, not a number. What infinity means in this context is that as we get closer to the limit, the value is always greater.

@StaticBlaster

16w↑1

I did all this in my head. No joke. I know the number to the left of 1 minus 1 must be negative 0.00001 (something like that) and the number to the right of 1 minus 1 must be positive 0.00001 so I can include the right-handed limit approaches positive infinity and the left-handed limit approaches negative infinity, so the general limit does not exist. Easy peazy lemon squeezy.

@alessandrogiglio5712

13w

Just a question, the given limit wouldn’t express the fact that the function, when approaching 1 from the negative side, goes to -infinity while approaching 1 prof positive side goes to +infinity?

@carultch

Yes. This is why the limit doesn't exist, because you get conflicting answers, depending on how you approach it.

In order for the limit to exist, all possible approaches have to yield the same result. For 1/x^2 when limited to the real numbers, both possible approaches yield the same result. But, if you account for complex number approaches, you get conflicting answers, and the limit doesn't exist.

@johnrine9671

11w

Very good! thank you.

@nour.ismail

17w↑1

I should have just quoted lindsay lohan in the beginning then!

"the limit does not exist!"

@mc4ndr3

17w↑1

The red marker is faint against the white background. Fortunately, the speech is clear and understandable, as with the other videos.

@user-sk7wr9mb9j

13w↑2

Loi de l'hopital laughing at the corner 😊

@macjarvis2882

10w

you cant use l’hopitals rule here unfortunately

@christophersoo

13w

everytime you have a limit question, divide both the numerator and denominator by x^n

@carultch

That works if you are looking at the limit as x approaches infinity, or negative infinity. You just compare the highest ordered powers of x, and ignore all the other terms. If they are both the same power, the limit as x approaches either infinity is the ratio of coefficients. A higher power on top, means it approaches one of the two infinities, depending on the sign of the coefficient and the net power on the ratio of x. A higher power on bottom, means it approaches zero.

For limits at finite values of x, it's the net multiplicity of poles and zeros at that point that matters. I.e. number of poles minus number of coinciding zeros. More poles than zeros means the limit doesn't exist; more zeros than poles, means the limit is zero.

@guilhermerocha2832

17w↑1

REally cool. Anyways, Merry Christmas!!

@bprpcalculusbasics

17w

Thanks! Merry Christmas to you as well!

@GokuTheSuperSaiyan1

16w

My immediate thoughts of the thumbnail; you need to see if the positive and negative limit are the sameb

@yoursleepparalysisdemon1828

havent taken any difficult math classes…. yet. but i just put in 0.5, 0.75, etc and could tell that diving something getting closer to 0 is infinity, but its infinity?

@wil-fri

17w

From a programmer POV is that, the smaller positive or the "smaller" negative number you can represent or show

@thetaomegatheta

17w

You forgot to finish your sentence

@danilonascimentorj

17w↑2

look at the boxes of black and red pens on the right.

@tomctutor

17w

Im jealous too.

@laurenproctor2896

16w

Great explanation! I was curious though, I remember learning to use L’Hopital’s rule when calculating indeterminate limits. Would this apply here? Using this rule isn’t the limit d/dx(x)/d/dx(x-1) = 1/1 = 1? Why does this give the wrong answer?