What is a Limit? Basic Idea of Limits
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- Опубликовано: 1 окт 2024
- Basic Idea of a Limit
In this video, I explore the intuitive concept of a limit, one of the foundational ideas in calculus. Limits play a crucial role in the development of calculus, enabling us to understand the behavior of functions as they approach a particular point. Without the concept of limits, many of the techniques and principles of calculus simply wouldn't exist! Here, I will walk you through the basic idea behind limits, explaining what it means when we write:
lim f(x) = L
x→a
and how this relates to the behavior of functions. While I won't actually compute specific limits in this video, I will help you understand how to approach basic limit questions.
What You Will Learn:
The fundamental concept of a limit and its role in calculus.
How to interpret the expression
lim f(x)=L
x→a
.
Visual and intuitive understanding of how limits describe the behavior of functions.
How to think about approaching limit questions without diving into calculations.
#Calculus #Limits #LimitIntuition #CalculusConcepts #UnderstandingLimits #ApproachingLimits #IntroductionToLimits #CalculusExplained #MathFundamentals #PatrickJMT #LimitConcepts #MathematicalIntuition #BasicCalculus #CalculusBasics #FunctionBehavior #MathEducation #Mathematics #ConceptOfLimits #MathVideo #MathIntuition
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Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other!
Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!
Exactly ❤️
@@madhugupta4178 Cant thank you enough :D
@@pt_2003 Anything
patrickJMT plz guide me how u make these videos
i mean how to make 5 minute video in 8mb
Please solve this one Lim tends to zero the rootover 2+x -rootover 2-x
And divided by x.
when you learn more math on RUclips than in math class
+SnoopGotTheScoop and you're paying £9k a year for these classes..
Bro can you tell me that where can i get chemistry videos
Mad Scientist Patrick had a vlog or something on here with his friends or so who have science channels on RUclips.
Mad Scientist Try Richard Thornley, RadioChemistry, or MSJChem
Mad Scientist( ak lectures)
congrats : )
those are great scores : )
imma give this comment a like just because
@@raanoooshh9296 hi
Thanks! :)
I remember studying calculus for my finals back in 2010. I had absolutely zero idea how I was going to survive that test. Someone told me about Patrick JMT and I remember binge watching his videos all night. Got an A+ on that test. Thanks a lot for getting me through calculus Patrick!
ha! nice! glad i can help : )
hug your monitor every time you watch a video
BRO I JUST ACED MY CALC EXAM PRIMARILY BECAUSE OF WATCHING YOUR VIDEOS! THANKS YOU SOOOOO MUCH
@@simpletn You're an ass:)
:)))@@simpletn
@Sir Iodine r/iamverysmart
@@theerisedhd8666 Try vector calculus, linear algebra, complex analysis, discrete maths...
You're the reason I survived pre calculus and am surviving ap Calc.. you sir deserve an award for making thousands of lives a lot less stressful ! THANK YOU FROM THE BOTTOM OF MY HEART PATRICK !!
@bac1087 tryin' to keep them short and sweet. my intent is not to fully teach the material, but to provide a short resource for all the hard working students out there when they get out of class.
Just became a Patron :)!
I'm a new teacher and have to teach calculus this year. First year teaching and your videos have been extremely helpful in re-learning the content and figuring out how I want to approach it with my students. THANK YOU!
ThAnks a bunch!
well, I am an old teacher and these videos have also been really useful. Thank you.
thank you alot my teacher you save my life you will show me some question
yeah iam sure that you are teacher but give me some question of this topic
@pennydave happy i could help : ) congrats on the great grade!
@vgadepa if you teach school or wherever you are, contact your system administrator and let them know you want access to youtube.
i mean, it is really stupid in the first place to block youtube ... yes, now the students will be productive while in the computer lab! youtube is the ONLY interesting site to a 13 year old... (wake up old people)
Thank you for being a sexy calculus beast.
It's making my summer just a bit easier.
Gaines
no, it is not in the works and will not be. too much piracy to make it worth the effort and the cost.
WOW. Funny story Pat, I failed grade 10 math back in 2010, grinded so hard and your videos just made everything make sense when nothing my teachers did.. 10 years later and I've graduated from a well recognized university with a degree in economics & finance. THANK YOU PATRICK JMT, the limit does not exist
@mrjj970 i am patrickjmt (as it says). i teach (on the internet if you watch my videos)
@PhoenixWright1000 i seriously doubt that : )
Sir, you are a legend. I appreciate your work very much.
@Musaibaziz behind what exactly?
that is because there was no problem to do
well l'hospitals rule uses derivatives, which in turn uses limits.
so... it is completely silly to use l'hospitals rule at this point.
ops, it looks like i may not have any vids with absolute value and limits... i will make some soon!
fo sho!
@blognewb and arbitrarily close is not generic and vague. it means: i can take a number an arbitrarily small distance away
you are welcome anyways
and yes, it looks like yours is undefined... although they do not have to be in general!
@usyflad how could there not be some dislikes? : ) it is the internets!
@baseball101star more than you can afford
@AlexandraBosRedSox happy that i could help :)
@8Trails50 looooooooool
@chiguy416 you are very, very welcome ; )
@blognewb arbitrarily close
@Wdec29 : )
@SuprSS787 perfect
@z7abib77z dividing by zero is always undefined.
I don't know how I start with your channel >> my level in math is zero . I want to became exellent in math for use in programming and solvig problems math and programming
my man patrick
use numerical evidence to conjecture a value for the slope of a tangent line to f(x)=sqrt(x^2+16) at x=3 how do I do this? This was on a limit test and I don't understand
@demifrost18 thanks :) give it 5 stars! :)
sure, no problem!
good luck!
Do you have a donation link?
If he does then i would definitely donate! :)
535Sandro on his site
Majed S click any video on my website, and a link pops up. thanks so much!
He's on patron. Google search it and search for him on there. Thank you so much for supporting PatrickJMT. He helps so many students.
The reasom for the equals is becase it is the limit of the said equation. the equation remains an equation. am i right?
u are very welcome!
I get it well. Thank you teacher🎉
This explains limits pretty well. An great video for those who are struggling with limits.
you save my life every year
@hedonism13 : )
Great video! You should make GMAT videos for the quantitative math portion!!!
My maths are diabolical.
You lost me after you approached my limit.
1 second. 😉
hi ms. foo's class.
Hi Patrick! You are an EXCEPTIONAL tutor honestly!! You got me through my first tough module at degree!!! 10000% you!
Can you please contact me regarding private tuition via Skype? I need you for this academic year!
Thank you Patrick! Your videos are very useful, I don't even have to attend my calculus classes :P.
Thanks for the clear explanations. By any chance do you have video where you have a graph and you reverse engineer an equation to come up with at least 5 limits to describe the graph shown?
Man, you are the best! I am doing integrals right now and back in this. You're doing god's work!
oh Jesus ! really appreciation ur service . wow
U are awesome Pat!
Ty for your vids!
I've watched tons of your videos & I've never said thank you. So thank you for what you do! My math classes are only 50 min. and most of my teachers have bad handwriting so I pretty much learn nothing in class, but when I watch your videos, I get it the first time. I never thought I would get an A in calc 2. I got a 98% on my final (the highest score in the class). A lot of it was my determination, but sir, I give half the credit to you. Thanks :D
Wow... truly amazing explanations of seemingly complicated mathematical concepts. I think I use your how-to videos more than I do the actual math lab at my school. Thanks for helping me maintain that A average in math!
you are a life saver ! math has never been explained so clearly ! thank you soooo much!!
omg life saverrrr #finals
Thank you so much!!! This is just awesome and I'm so grateful for you making these available.
अपने हमे बहुत अच्छा समझाया । हम अति खुश हुए । शुकरिया ।
मैं राय में आप के साथ सहमत
गांडू, इंग्लिश में बोल ना !!!
Thank you so much for your videos. I had this stuff 40 years ago and still enjoy it. You're a great teacher Pat.
You are the freakin bestest
Thank you so much for posting this! I am having such a hard time reading and understanding the graph but you other video was a great tutorial!
Hello sir ! Could you share me some experience how to record this video ?
@markoicu93 my pleasure. you must dedicate your next quiz to patrickjmt!
ahhhahaha : ) maybe not the nobel prize... maybe just a 'nice guy award' or something : )
I wish you would put highlight links or boxes over the a) Factor , b) Common Denominator, c) Expand, etc... this way I could just click it and view the video.
I like the way he says "plug and chug"
Awesome video. I'm taking an online calculus class. Resources outside my book are a must
Ohhh my God thank you very much I couldn't understand it until you explain it!!!
thanks man.
You have helped me a lot.
@patrickJMT its funny how once I got to percalc my textbooks became useless basically. tutors are way too expensive, and I always end up using youtube and get so much more of a better understanding than my lectures where my professor goes insanely quick. used my textbook in 1st 1/2 of semester and had about a C- average, in the second half from your videos I was able to raise my grade and ended up with a B.
I teach prep algebra and now have to take calc. It is like a foreign language to me. Your videos are helping. Your shortcuts and tricks are right up my alley.....thx
✅
bruh i was 1 when this dropped
you are 15?
Hey Patrick! I finished calculus thanks to you and I am horrible at math. No more math for me! Thanks a lot!
Great explanation ... however lim x -> 5 (x - 4) is equal to 1... it is not deceiving in any way. Why is it?
your vids are awesome , i hope u get more than a million subscribers
@wolf92193 keep watching the videos in that case! : )
1:26.
A minute and 26 seconds to acheive what all my teachers and Khan Academy couldn't do in weeks.
It was just like "OOOHHHHHH..."
As the video "approached" 02:15, I "approached" understanding the concept....for the first time...
Patrick you help me in calculus when I was in university...thank you
What is a limit? I do not understand the deeper concept. I can find a limit on paper, and I can see where it is when I look at a graph. I can do the math just fine. But what actually is it? What does it do? Please don't talk about equations, that's not the kind of answer I am looking for. I know how to find a limit. I want to know What does a LIMIT DO? I want to know if my thinking is correct? IS a Limit a Prediction of WHERE one might expect a point to be located on the graph of a line.
The circumference of a circle is r-√(2r^2)/2 +√(2r^2) - (r+1) /2
If r is even then= r/2
If r is odd then = (r+1) /2
You can teach me 8th class math plz kV school
Hi Patrickjmt , why not make GRE videos for people preparing to apply for graduate school ?
VERY MUCH HELPFUL
Hey mate thanks for the video. Just one thing, at 1:40 you talk about the confusion around the "=1" and that it is increasing to 1 instead. I would have thought that the "=1" is in fact correct as it denotes that 1 is in fact the LIMIT for that function and represents the upper/lower most value. If we were to think of the function approaching 1 then there is no distinct upper/lower value to consider and therefore has no limit. I could be splitting hairs but wanted to clarify that it's correct!
Hey Patrick can you PLEASE make a video on the epsilon-delta proof of a limit? I just really want to understand it, I looked at my book and it was hard to understand, I mean it looked weird, I sort of see where they are going but I am still very lost. I looked around and I don't think you have made a video on it, can you please make one, you explain things very well and I think you will be able to explain it.
@Machammerballs its usefull for finding the slope of a curve. If you try to find the slope of a curve with a regular slope formula, you get either an "average slope" or 0/0. limit lets u see the slope just before and just after the point u want the slope of, so u can see what number the two slopes (before and after the point) are approaching. there are other uses too, like if the function is undefined at the point you are looking at you can superimpose the limit of that point, n' continuity stuf
Hey Patrick!! Which is the video which introduces integration??I am not able to find it...Thanks in advance
I don't know how I start with your channel >> my level in math is zero . I want to became exellent in math for use in programming and solvig problems math and programming .
Ah man. Your videos help me pass first year maths but that's what every ignorant hipster or lazy developer says. Game companies compete with piracy and yet still develop games for Windows & now, more prevalently, Linux. Please do an Android app. Anyways, keep up the good work, you're like a private tutor for many students here at the University of Stellenbosch in South Africa.
He means piracy in the fact that other developers will put out a close-to-identical app for free, which might not be taken down quickly enough from google play. Apple's app-procedures are currently stricter. However, i dont understand why he wouldn't make an add-supported free version. In that way, he will come out on top regardless.
You mean the exact same piracy possible on the iPhone?
It's too easy to "Jailbreak" iDevices now. You can literally click a button while it's plugged into your computer and it does it within seconds. You should just make an Android app. Think about how many people are missing out because there isn't an Android version.
I think you are wrong when you said that the notion is deceiving because in your example when you take no. close to 5 its maximum limit is 1 not that when x stands to 5, f(x) should stands to 1 no its maximum limit i.e the maximum value of f(x) is 1. Please correct me if i am wrong. By the way amazing video and thanks a lot for the upload !!!
@patrickJMT you're wrong.0/0 does not equal undefined. it's an exception for the rule that anything over zero is undefined. 0/0 is a special becuz zero over anything equals zero but any number over itself will always equal one. this have the characteristics of all 3 but they are all contradicting so u actually gotta do something more to the equation.
Hi, patrick
I wanted you to know that this is a good explanation of the limit, but it would benefit a lot of people if you explained the arcane "Delta epsilon" proof. AKA the formal definition of the limit, I was pissed off because it was the only question I missed on the test.
Thank You for all your help.