Solving the Math Calculus Problem in Mean Girls
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- Опубликовано: 11 ноя 2023
- Let's solve some limits!🚀 in this video I show you two solutions as well as a graphical solution to why 'the limit does not exist'!
For those of you that are new here, hi there 🌞 my name is Ellie and I'm a Cambridge Part III Mathematics Graduate and current Astrodynamics Software Engineer! This channel is where I nerd out about maths, physics, space and coding so if that sounds like something you're interested in, click the subscribe button to follow along ☺️
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I love when they show us more than one way to solve a problem. Amazing video!
Amazing video! You’re so fluent at explaining your approaches while evaluating the problem. Always great to see another enthusiastic mathematician.
Thank you so much!!
@EllieSleightholm Thanks for sharing Elkie. I really hope you can PLEASE respond to my other.comment/question about math whenever you can. Thanks very much
@leif1075 what was your question? Sorry I can’t seem to find it! ☺️
@EllieSleightholm thanks. I'm sorry just that would you agree even Ramanujan struggled and had tonwork hard and math is just one type of intelligence and not a superior kind necessarily. Thanks for answering
@leif1075 I couldn’t make an opinion on Ramanujan because I’m not him. However, I don’t agree that any mathematician should be considered superior for just having studied mathematics! You can’t do great things without working hard! I studied maths at Cambridge and I put that down to work ethic and drive rather than natural intelligence. Hope that helps answer your question!
this was unexpectedly fun to watch. cant wait for more!
Haha thank you!!☺️
me taking geometry having no clue about any calculus watching this:
A kind of one step solution you could devise is using certain approximations, namely as x goes to 0, ln(1+x) -->x , Sinx--->x, applying this you immediately arrive at the result -2/x
Awesome 😎
this is basically using the results from the Taylor expansion
That is actually a standard technique I was taught and that I cover in my calculus classes. Understanding relative orders of growth of different functions can be a really helpful technique. It shows up in more than just calculus too.
this only works correctly if we have multiplication
Found the engineer
No need to use l'Hopital or Taylor or even to know derivatives. Just factorize 1/sinx and divide by x numerator and denominator : [ ln(1-x)/x - sinx/x] [ sinx/x] -> -2 (all well known elementary limits). Then we're left with 1/sinx, whose limit to 0 does not exist obviously.
you generally use derivatives to derive the well-known elementary limits that you mention
@@hach1koko They are called "elementary" for a reason. the limit of sinx/x can me solved using a trivial geometric inequality, and the limit of ln(1-x)/x can be written as ln (1-x)^1/x, and then solved with the definition of e. No need of derivatives at all.
You just made it look so easy, I like your videos and I wish you could do more calculations.
Thank you so much!!
Thanks very much one of the best RUclips channel i have seen so far)
Thank u, you're such a great content creator ❤❤
i was solving integrals just now and this come into my recommended, so I randomly clicked to see if I can solve it. i did not disappoint myself :D
I like the Taylor solution (infinite series) as it shows the behavior of the functions as the limit is approached.
Would have loved if you'd given the general rule for L'Hopital. For anyone wondering: On the slide about LH rule, it is stated that lim f' / g' needs to exist. This is not necessary, otherwise her first method of proving the non-convergence of the limit does not hold. If A -> B, we can not infere B - > A, e.g. if it rained we know it is wet outside, but just because it is wet outside doesn't necessarily mean it rained; it could have been the neighbour watering the garden or whatever.
Otherwise, good explanations :-) I liked the part about the series expansion. Although you could have mentioned it is important to investigate the smaller order term because we approach 0.
love the rotation matrix in the background
Loved it!
I recently found your channel and you have become such an inspiration for me. I'm planning on studying Math at university next year and your channel makes me even more excited to start than I was before ! Thank you for all the great math content you're truly awesome !
thank you so much 🥺🥺 that means so much! Eeek maths at uni - definitely do it!! I absolutely loved it!
I used to call them Le hospital and Laplace transformer back in college
You could also multiply and divide the entire thing by x, then you could use some famous limit identities to remove the indeterminate form. Great video though, thanks for sharing!
I have just subscribed your channel, and I found wonderful contents. I am about to start my masters degree in computational science and I am waiting for your videos regarding more computation videos.
omg this is such a fun idea!!!
This is the kinda content I would watch to help me go to sleep. Fantastic. Thank you for curing my insomnia 💋
You’re most welcome 🤝🥰
This is the kind of thing that keeps me up at night (in the best way possible, but still)---I always get sucked into doing one more problem until it's like 2 am...
Wish I had your determination in solving problems till late in the night lol. I just go to bed leaving the problem unsolved if I’m tired enough(which I am so often)
This was great, i got the same answer using 'l hospitals' rule. Can you please do 'Gifted' next? although i don't think i will be able to understand any of the maths involved😅
‘Gifted’ coming up! ☺️
Omg I'm just starting AP Calculus AB and you've made the explanations so succulent and clear that I can understand! Massive props to you!
Please more videos like THIS thanks)
Fun fact: If you have a * instead of a - in the numerator (e.g., ln(1-x)*sin(x)), then the limit is -1, as the first girl answered.
A few days ago I watched a low-quality video showing that math contest scene, and I did think the minus was a times. I was very confused when the first girl's answer was counted wrong.
In the new Mean Girl film they mess up the question instead of tending towards 0, they set it tending towards 0+. So would tend towards -infinity.
hi, i am new on your channel, and i was hoping you could give some advice on where to start on College Math topics (i am a high school student, currently on the last year)
Could you please explain the time variable in a Bézier curve? As it is incramented / steps through in a program loop, please. Thanks.
Awesome Video! But I have one question for the Taylor-Expansion. At 7:09 where u simply the terms I don’t get why u don’t scare the down part. Wouldn’t it be -2/x^2 at the end rf am I seeing something wrong? Thank u!
I must admit that I didn't know the Taylor series expansion trick ... Great video 😊
Thank you so much☺️
I think the Taylor Expansion approach requires much more explanation. It works because we have a limit at zero and higher powers approach zero much faster (when we are close to zero). Even then there is an infinite number of terms and "zero" added infinitely many times is not necessarily zero.
I like your style, it's quite ASMR-tist. Just suscribed!
Please explain the functions and limits, differentiation, integration my exam is coming in December
The Taylor series expansion part was cool, I like seeing the Taylor series find its way into anything and everything
Need more videos(solving problems not from movies necessarily) like this please.
I have no clue what’s going on but I love it
Harika şeyler hissettiriyoo ❤
This is so interesting 🫶🫶
Please can you tell us how we could start studying mathematics.
I follow you from Egypt thank you for your good videos❤
amazing video
I just thought the parts, graphically,, as in what would (around 0) the graph of ln part and if sinX is + or neg from the left or right of 0, and how 1-cos² would be pos or neg. But first what is value of y at x=0 plug ins, for reference. Which I used basic graphs of sin, cos and ln to see if there was a simple route. I haven't done math since HS Advanced Placement Calculus in 07/08. So I thought 'the graphs' and how sometimes knwoning simple graphs can show what complex equations will follow,, at least at like key points (like using unit circle of Quadrant I for the other 3 Quadr. with trig. functs.
I didnt visualize the whole graph, just at what was being looked at.
Thanks mammmm
Sorry if this is terribly dumb, but what writing tablet and computer program are you using? Looks great
do you use the goodnotes application?
How do you know the limit DNE or is infinte just based off the first L'hopitals rule can't you use it again? (how do you know when to stop?)
What's your review on jee advanced mathematics ( an entrance examination for IIT IN INDIA)
You are brilliant❤
Thank you so much 🥹
What app did you use to do this? looks really helpful for notes lol
Not sure but it looks like it could be notability to me
Fun video, UCSD math major here
Why didn’t you switch 1-cos^2(x) to sin^2(x) using trig identities? I would think that would simplify calculations
I did if you watch the whole video :) didn’t really matter that much for the L’Hopital’s rule as it doesn’t simplify things that much.
Hallo Ellie! How are you? Question: Why don't you make videos about:" Introducing the LIMITS"? It would be helpfull...
Hey Laura, I’m doing well thank you! Hope you are too! That’s a good idea! I’ll amend the title ☺️
Could've also just repeated L'hopital, but I get it's a pain to differentiate over and over hahaha.
what software do you use?
A level maths you haunt me again
I'm curious why you didn't use the pythagorean identity in the denominator: sin^2x + cox^2x = 1, therefore 1 - cos^2x = sin^2x. Might make it easier to derive
@hollystanleyy if you watch the full video, I do that in the Taylor series expansion! The first method doesn’t really matter too much as there’s only an extra 1 🚀
For the first limit you could also approach it to break up the expression to ln(1-x)/1-cos^2(x) -sinx/1-cos^x the first term obviously goes to 0 and the second term simplifies to -sinx/sin^2x which further simiplifies to -1/sinx which goes to 1/0 as x approaches 0 this is DNE. I think this is the approach I would take if I were doing a limit bee.
I’m not sure if that’s a valid argument, since you can only split the limits in an addition if they themselves converge and that’s broken here.
@@jefftimer1752 I think it is valid, I think it is invalid to do so if it were multiplied or divided. However seeing it is literally a composition of two function being added if one is D.N.E. it should fallow that the whole equation is D.N.E. as you would only use l'hopital when you get something like 0/0 or ∞/∞.
Just graduated with a 4.0 GPA in electrical engineering and I do have to say, from the first 30 seconds of this video, I can tell your a legend. In my graduating class of 73, 70 were men and only 3 were women. It always is awesome to see women who actually try in stem. This channel is like a glimpse of a parallel universe showing what a world without representation/work ethic problems would look like. Like at my first internship, out of the 30 interns in the prestigious research facility, all 30 of us were men, with around 70% being white, 29% hispanic (and out of them, most were whitish like myself lamo XD), and then 1% black (one guy looked black but he was mixed, so not even an actual black guy). But yeah Elli, you are amazing. People like you are what fix the world both technologically and politically. You really are amazing, so please keep up the good work!
May i ask you about the app ur using in this video?
Goodnotes on my iPad :)
I am trying to self taught Multivariate calculas, Probability and statistics, Linear algebra for AI research, please recommend books for it
I’ll do some research and get back to you ☺️
Thomas Calculus
Introduction to Linear Algebra by Gilbert Strang
Those are some undergraduate materials for Multivariate Calculus and Linear Algebra
7:40 is the series in the denominator sin or sin squared?
Sin squared but there’s a division by x to get it to the form before the -2/x part :)
I seem to remember that The Simpsons also had math included.
Movie math suggestion: Prove the Snake Lemma! It’s in the film It’s My Turn.
Oooo I’ll take a look!!
@@EllieSleightholm Great! Hope to see a future video on it!
What do you mean by leading order terms? (7:30)
the terms with the largest order of magnitude :)
Thank you Ellie from Cambridge. Do you also have videos on Calculus II integrals, III multivariables and Linear Algebra?
Ive been thinking of making a how to video on mjltiple math provlems as I progress from algebra to trig to calc. If you do so, I'd recommend a large plexi glass / glass window with an $80 Rhøde lapel mic. 😊
i would use maclaurin series because of x->0
متابعكي من العراق ❤
just a note, graphs would be useful to visualise
Or... like I prefer to sing
No no, no no no no, no no no no, no no there's no limit!
Since my musical references apparently are 30 years old...
ruclips.net/video/r6FVk2k4qsM/видео.htmlsi=R_EAAwPFf7Sd6y3D
did u watch the new mean girls musical because the limit they showed does exist since x tends positif zero, can you please check it out and make a vid about it cuz no body talked about it
Hi, why infinity has a + or - value? Isn’t infinity by its definition a large number which is unlimited
positive infinity is a really big positive number and negative infinity is a really big negative number.
exactly what @monkalina6264 said! ☺️
Thank you .. infinity is an unknown and strange no ( if it can be defined as a number )
If you add 1+Infinity =infinity which mathematically is incorrect
@@georgecimpoeru6052
Infinity is not a number it's an idea or concept. Nothing can be equal to infinity. When we say that it just means it tends to infinity.
I used to just cheat and plot the graph on my computer. Of course, this was the 1980's so I had to code my own graphing software on my ZX Spectrum because nothing existed. Then I got a graphics calculator in the upper sixth and my first homework I turned in I got zero for a whole bunch of questions as I hadn't displayed my method and he now knew I had computerized graphing capability in the form of a graphical calculator. Apparently, it didn't matter when he didn't know 😃
l'hopitals or pythagorean identity was my first thought
This is brilliant… it reminds me how stupid i am 😏
Very smart and pretty girl
The amazing solutions for not existence of the limit this function. If you users sequencies for proof the not existencie this limit is possible? Users sub sequencies for examble. Thanks
It would not give much advantage to try finding a particular sequence of values for x as you would still need to consider the behavior of the log and trigonometric functions. Those two types do not typically behave very nicely together.
Can you increase the audio please it's very difficult for me to hear. 😊😊😊
اسطورة❤
Nice ma'am
Omg I feel so dumb 😭😭😭❤❤❤
ellie ı have a question . Are there any math books you would recommend to us?
It can be a topic related to mathematics lessons
I’m thinking of making a video giving people books and resources to help learn mathematics - stay tuned!☺️
@@EllieSleightholm ım gonna wait for that video 🧐
teacher ım waitting your video . ı ll buy a few books
@@BurakSimsek-kf2xl😮😮😮hoçam
Please make a video on 7 millennium problems
i see you are about as fun at partys as me
😂😂😂
You have a soothing voice. You should do ASMR video.@@EllieSleightholm
try the problem from the beautiful mind there is tree digarm problem
Sorry the movie is called Good Will Hunting not a beautiful mind
@@user-lu6yg3vk9z that video is coming in 2 weeks - stay tuned!!
Personally, I would use the Taylor series approximation
Can you make a video please reply?
3:00 - Correction/elaboration: If a limit evaluates to a point at infinity in an extended space of real numbers, then it doesn't exist in R, and, as such, the function is divergent in R. However, it exists in that extended space of real numbers and the function converges within such a space.
'A limit is infinite or does not exist' can just as well be rephrased as 'a limit does not exist in this particular space', as we can always find a space where a function or a sequence that we are dealing with converges, it just might not have some of the nice properties of a space where the relevant elements are from (for example, it might not be metric, like most of the extended spaces of numbers, or it might not be Hausdorff in the case we have multiple accumulation points).
This particular limit does exist in the extended real line with just one point at infinity (let's call it 'inf' or 'unsigned infinity') with the usual topology, doesn't exist in the extended real line with two such points ('+inf', '-inf') with the usual topology, and does exist in the extended real line with three such points ('inf', '+inf', '-inf' - this space is not Hausdorff) with the topology that you likely expect.
So, yeah, there is definitely a limit here if their existence in any of the extended real lines counts (otherwise there wouldn't be a need to evaluate whether or not 'a limit is infinite or doesn't exist', as 'infinite limit' is not a thing in the space of real numbers). Considering that the extended real line with just the 'inf' is one of the standard ones, I see no reason to give priority to the one with just '+inf' and '-inf'.
Hell, if we can just consider any spaces, there are such where there is lim(sin(x)) as x->inf, such as ones where there are points whose neighbourhoods always include the line segment [-1, 1].
Also, just in case, because you imply that a function can have only one limit at most, consider a mapping from any space to a space with anti-discrete topology. Such a mapping is guaranteed to have a limit within that space (i.e. no extensions needed), and it is even guaranteed to converge to every point in that space, all at once. Any function or sequence can have such a property if we are dealing with non-Hausdorff spaces.
If you do lhopitals rule twice it results in -1/2
You can only do lhospitals rule when both the bottom and top of the limit are both either (pos or negative) infinity or zero. Notice after doing the rule once the top doesn't fit this rule, meaning you can do the rule again.
i think you did a mistake in taking the derivative
JEE STUDENT : 9min waste kardiya
What happened to the negative behind 1/(1-x) at 2:27 ?
Nice video an explanation. I like when stories in entertainment tie in with a mathematics lesson. Cheerful calculations 🧮.
It's just a simple problem🥲
Simply using eaualents ln(1-x)〰-x, sinx〰x, 1-(cosx)^2〰(x^2)/2. In russian university if you use rule Lopital or rows Taylor and don't know equalents you can't pass exam. Task given you to use equal and you must owe this method.