Limits and Limit Laws in Calculus

Подписаться 3,3 млн

Просмотров 227 тыс.

50% 1

In introducing the concept of differentiation, we investigated the behavior of some parameter in the limit of something else approaching zero or infinity. This concept of limits is how calculus got started. As the field developed, new techniques arose such that we don't have to find limits very often anymore, but we still use them sometimes, so let's make sure we know what they are, how they work, and how to evaluate them!
Watch the whole Calculus playlist: bit.ly/ProfDave...
Watch the whole Mathematics playlist: bit.ly/ProfDave...
Classical Physics Tutorials: bit.ly/ProfDave...
Modern Physics Tutorials: bit.ly/ProfDave...
General Chemistry Tutorials: bit.ly/ProfDave...
Organic Chemistry Tutorials: bit.ly/ProfDave...
Biochemistry Tutorials: bit.ly/ProfDave...
Biology Tutorials: bit.ly/ProfDaveBio
EMAIL► ProfessorDaveExplains@gmail.com
PATREON► / professordaveexplains
Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!
Amazon: amzn.to/2HtNpVH
Bookshop: bit.ly/39cKADM
Barnes and Noble: bit.ly/3pUjmrn
Book Depository: bit.ly/3aOVDlT

Опубликовано:

28 сен 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 151

@crofregernish4695 4 года назад

Trying to do calculus online for a college course where the professor only teaches what's literally in the book (no further explanations) This was so helpful!!!

@jonathanjohnny225 6 лет назад

he knows a lot about science stufffff, science jesus explains

@lits0_042 5 лет назад

this is mostly math

@satrickptar6265 5 лет назад

@@lits0_042 but math is science

@lits0_042 5 лет назад

@@satrickptar6265 no, one helps the other

@satrickptar6265 5 лет назад

@@lits0_042 Science is the main seed, math is just a branch

@lits0_042 5 лет назад

@@satrickptar6265science is the human interpretation of math

@billcook4768 2 года назад

Random trivia: One of the examples in this video is that limit x-> 0 of sin(x)/x = 1. Seems simple here using a graph or calculator, but this is one of the most important “facts” in all of math. Not necessarily in this form, but in equivalent forms such as the idea that if x is “small”, sin(x) is approximately equal to x.

@krishnannarayanan8819 Год назад

Engineer Theorem??

@kontiimanalatit8987 Год назад

@@krishnannarayanan8819physics use it too

@jaydevpandey9877 5 лет назад

you are very good at explaining all science stuff thank you professor Dave

@kavyahegade6477 4 года назад

None other than you can teach like this😊.. you're amazing and unique 👌don't know how many times i passed the exam by watching your videos🤝🤝

@slickyy21 Год назад

Where is the comprehension check?

@dimitriosmenounos1009 5 лет назад

Congrats! You explained it very well.

@MOizSUAVE14 6 лет назад

dang i wish i watched this video before my 1st exam.

@DarinBrownSJDCMath 4 года назад

11:51 cancelling factors, not terms

@MathCuriousity Год назад

I have to say Dave used the word parameter incorrectly; this word means either a constant such as a particles mass, or it can mean a function of two other functions such as if we parametrized the unit circle for t and said y=sin(t) and x=cos(t)

@khalolyyan7971 3 года назад

Could you please make a video about the precise definition of limits ( epsilon and delta) thank you in advance!

@robertwood2424 Год назад

8:45 Lim f(x)=6 Lim g(x)=2 Then it goes to lim[f(x)-3g(x)] =6-3(2)=0 Why is g(x) now being multiplied by 3, instead of 6-2=4?

@Jesuisunknown 7 месяцев назад

My tiny brain is going to expload 😆

@pfever Месяц назад

9:57 this could have been explained much easier. Wherever you have f(x) you can replace by lim f(x), and wherever you have x you can replace it by a.

@srinidhiav 5 лет назад

Very nicely explained!! 👍

@dakshbadal7522 4 года назад

If you want him to make money but can't afford patreon, just watch half of the unskippable ad. If you skip the ad asap, no money goes to the creator.

@matokurin 3 года назад

Very very kind. Thank you

@williamadams137 5 лет назад

6:00, is that the unit step function

@lahiru1k 7 месяцев назад

Thank you❤

@ephremephi2501 3 года назад

thank you

@thestoryofmylifesearchingf9631 11 месяцев назад

YESS FINALLY I GOT IT THANK U SO MUCH

@ummahyehmmm7403 3 года назад

That was such a help 😫 thanks sm

@MathCuriousity Год назад

Anybody know what program he used to create these videos? Also what program do I need to "record" the videos or are they automatically recorded by the same program? Thanks!

@aselim20. Год назад

I wrote it.

@joschaberg6940 3 года назад

I don't see why laws 6 and 8 require a positive integer for n. For example I could plug in 0 for n and don't see where an error happens. Clarification would be much appreciated!

@erikawwad7653 3 года назад

What if the limit is 0? 0^0 is 0/0 and you cannot divide by 0!

@erikawwad7653 3 года назад

Little algebra: 2^2 is 2 * 2, 2^1 is 2, thus 2^0 is 2/2

@erikawwad7653 3 года назад

in addition, roots are 1/n powers. The square root of 4 is 2, since 2^2 is 4. What times itself 0 times yields a number? How do you multiply 0 times? This would be the 1/0 power, or multiplying infinite times if we choose to evaluate the limit of 1/x approaching 0. Thus the second rule does not hold for 0

@erikawwad7653 3 года назад

see how this logic cannot be applied for the last 2

@joschaberg6940 3 года назад

@@erikawwad7653 Hi Erik, i didn't raise any complains about law 7) so no worries concerning the 1/n powers. :) As for your excellent question "What times itself 0 times yields a number?" I agree, that this doesn't make sense. But that does not mean that b^0 is undefined. You are correct that for a positive exponent b^n is equivalent to the product of n times b. However, the power b^n also has a reciprocal 1/(b^n). It is also be written as: b^(-n) Now what is b^2 * b^3? It is b^5 This actually generalises: b^n * b^m = b^(n+m) And now you might answer what: b^n * b^(-n) is equal to. Dave has a great video about that as well btw: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-K_TD9GuP9uQ.html

@tGoldenPhoenix 2 года назад

Done.

@teekay9498 9 месяцев назад

These are great information but the videos are not organized making things hard

@Chriss123HD 5 лет назад

you had me at x

@benquinney2 4 года назад

Infinitesimal

@hareecionelson5875 3 года назад

Ahh, so even though f(0) = 1 when x>= 0, the limit of f(0) depends on the direction, since the limit of f(x) is not always = f(x)

@ericpham4011 4 года назад

The real dificulty is that we are using physical law and logic to measure a sensitive being of truth and super natural reality. In graph we can draw and the graph would touch but in uncertainty priciple Prime chemistry and quantum probabilty it is imposible to touch the face Prime God

@kbailkeri 4 года назад

What

@eigentlichtoll02 5 лет назад

only watch this for the intro

@bushbuddyplatypus 5 лет назад

It really doesn't get more boring than this.

@qualquan 6 лет назад

Yada yada yada. Unless you learn what is and how to eliminate the "averaging error" during differentiation you have learned calculus as a religion, and not as a science. BTW never mention 0/0. Its about as respectable as invoking God in science.

@ProfessorDaveExplains 6 лет назад

I'm not sure that you know what a religion is. Math can never be religion, because math does not contain dogma. Math also is not a science, so I'm not sure you know what science is either. Never mention zero over zero? I have no idea what you're talking about.

@sunithavs8901 5 лет назад

You just reveled to people that you are dumb

@mrmoth26 Год назад

Dave, you truly have no limits.

@jashansehgal7347 5 лет назад

You are the best teacher. Please do not leave this channel ever I really consider you as my mentor because u are unfolding the fundamentals

@vasanthisuperkaruna3407 3 года назад

exactly. none in the world teaches like him. beautiful explanation indeed!!!

@NewWesternFront Год назад

i'm putting a giant portrait of Dave in my living room. I will stare at it everyday

@RazorM97 5 лет назад

People who disliked this video have no limits

@dariustbt6840 5 лет назад

There are no limits for science jesus!

@salonisharma2807 6 лет назад

Thank you sir your all videos have cleared my concepts! 😊

@ahmadmukhtar5538 5 лет назад

He explains great Saloni

@destinyovbiebo8988 4 года назад

You like math?

@vasanthisuperkaruna3407 3 года назад

@@destinyovbiebo8988 Math is important for indian students giving jee, nda and so forth

@melontusk7358 4 года назад

I've been wondering about why the formal definition of a continuous involves a limit for such a long time, and the epsilon-delta definition didn't help either, but this video lecture really made it crystal clear to me. Thanks so much.

@typalfi7139 5 лет назад

You are good at explaining Professor Dave. Thankyou!

@tomsdailystudy 2 года назад

Thank god. I thought I lost Professor Dave since last semester. Just subscribed so the search is way easier. Good stuff on this channel. And for whatever reason it’s also a fun channel which makes learning easier.

@GavinLon 5 лет назад

This is a very clear explanation. Thanks Professor Dave.

@hansisbrucker813 5 лет назад

Wait. Since when are limits defunct? I thought they replaced infinitesimals in calculus

@ProfessorDaveExplains 5 лет назад

well they still have application, it's just that we don't need them to take derivatives.

@hansisbrucker813 5 лет назад

@@ProfessorDaveExplains oooh ok. Thanks

@thefact6225 3 года назад

Proffecer:"0/0 could be doing anything" 🤣

@kamalaambika9520 6 лет назад

He knows a lot about different stuff, science Jesus here explains !^_^

@jamesmccreery250 4 года назад

Why did this take 3 weeks in Calculus class? No offense Garry, but I think Dave is smarter than you.

@floweytheflower5261 7 месяцев назад

5:29 AAAAGHHH IT'S ALL 0.017!!!

@weebo1926 2 месяца назад

the sine function depends on degrees being used, if you use radians, it will give the right answer which is close to 1, do not use degrees for this operation.

@sagar-uj1nb 4 года назад

your videos are awesome sir. I think you are referring to stewart calculus book for example problems....

@camellemons3737 5 лет назад

i need to know how many of that shirt you have. and if it is 1 what happens if it gets worn out?

@meltdown6856 5 лет назад

So a limit just tells us what a function would normally do as x approaches a value on the x axis rit? ( Pls correct me if I am wrong)

@ProfessorDaveExplains 5 лет назад

yep!

@adeboyebamgboye2486 2 года назад

This is perhaps the most important thing I learned from the video...Like the idea wasn't exactly conceptualized before I started taking in the laws. Thanks!

@reanwithkimleng Месяц назад

Dear sir could you help me please ❤❤ 😊Limits and Differential Calculus @ Introduction to limits, continuity, and importance @ Techniques for finding limits and understanding continuity @Differentiation rules (power, product, quotient, chain) and techniques @Applying derivatives: optimization, related rates, motion analysis @Multivariate calculus: partial derivatives, gradients, optimization 😊Calculus in Machine Learning @Role of calculus in ML: optimizing cost Functions @Gradient descent: derivation and implementation @Backpropagation in neural networks and derivatives @Advanced optimization: SGD, Momentum, RMSprop, Adam

@apothe6 4 месяца назад

The first question of why don't we just plug the value in is exactly what I was wondering.

@matthewlepage1253 Год назад

Thanks!

@barcinnicrab9562 2 месяца назад

Amazing explanation really nice to hear :) Everything makes sens

@lakewobegonesbest8725 21 день назад

Such an easier way to understand, thank you

@gaminisiriwardana5946 4 года назад

excellent way of explaining. I got amazed with your explanation and did lot of calculus sums. Sir I will be sending very special 4 questions through email to you. Please be kind enough to reply. Interestingly waiting for your explanation . Thanks

@farhanahmed2508 6 лет назад

Love this!

@hosinsinaga4694 7 месяцев назад

can you tell me what aplication you use draw all graph?

@slowfern Год назад

lol i just realized singularity in a black hole is the same thing as discontinuity here

@theteenengineer7589 4 года назад

i think they teach that in high schools here in canada, its good to understand them before i get there :):):)

@EfeAikpokhio 2 года назад

Wow, this was amazing! Thanks Professor

@ronaldjorgensen6839 4 года назад

I WILL PAY YOU ASAP DAVE THE MATH DEMANDS MY LUCK MUST CHANGE

@ingvark1968 5 лет назад

I just agree to all the roses below

@santoshgujar5237 7 месяцев назад

✨Thank you, Sir, 🙏🌺✨

@ankitaaarya 5 лет назад

3:00 no one ever told me that, thanks

@ankitaaarya 5 лет назад

Discontinuity

@harishgehlot2020 2 года назад

I am from India 👍🔥☺️

@rishik-w1j 6 месяцев назад

Thank you

@manismanai2276 6 лет назад

Your helped me to pass in my exam.

@asheshmandal4952 6 лет назад

Thank you sir

@drakulaki1380 5 лет назад

Thank you professor!

@supercheese8663 2 месяца назад

this might be weird to comment on a calculus video but I only passed Further Linear Algebra because of your videos. Just wish I watched this playlist before my calculus exam.

@SÀN-D-MAN 6 месяцев назад

Professor Dave here, let's take about limits 🔥🔥🔥🔥🔥

@Kiky_MedPhysicist Месяц назад

Thank you sir for your dedication and for making this free!

@kontiimanalatit8987 Год назад

Good explanation about limits, but you didn't delve into the important limits or methods about calculating limits, which aren't just f(a) (like factoring highest powers in denominator and numerator or 1/infinity 1/0 forms, which are considered as 0 and +inf)

@engnrrmuhammadali7453 4 года назад

Sir upload video over contuinity please help me sir.....

@KristineOjide 2 месяца назад

7:09

@fernandoportal5422 Год назад

Min 10:25 I was thinking why not just graphic the function but now, i get why not

@kriswillems5661 Год назад

You should have mentioned that both limits need to exist for the limit of a sum to be the sum of the limits (if they don't exist the sum can still have a limit).