Limits and Limit Laws in Calculus

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!
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[@crofregernish4695]

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!!!

[@jashansehgal7347]

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]

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

[@NewWesternFront]

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

[@mrmoth26]

Dave, you truly have no limits.

[@jonathanjohnny225]

he knows a lot about science stufffff, science jesus explains

[@lits0_042]

this is mostly math

[@satrickptar6265]

@@lits0_042 but math is science

[@lits0_042]

@@satrickptar6265 no, one helps the other

[@satrickptar6265]

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

[@lits0_042]

@@satrickptar6265science is the human interpretation of math

[@melontusk7358]

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]

You are good at explaining Professor Dave. Thankyou!

[@tomsdailystudy]

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]

This is a very clear explanation. Thanks Professor Dave.

[@jaydevpandey9877]

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

[@billcook4768]

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]

Engineer Theorem??

[@kontiimanalatit8987]

​@@krishnannarayanan8819physics use it too

[@dimitriosmenounos1009]

Congrats! You explained it very well.

[@salonisharma2807]

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

[@ahmadmukhtar5538]

He explains great Saloni

[@destinyovbiebo8988]

You like math?

[@vasanthisuperkaruna3407]

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

[@srinidhiav]

Very nicely explained!! 👍

[@Pinkie4]

Wow, this was amazing! Thanks Professor

[@drakulaki1380]

Thank you professor!

[@shubhamjoshi9624]

Professor dave is just so good and all rounder in field of science.

[@slickyy21]

Where is the comprehension check?

[@matokurin]

Very very kind. Thank you

[@farhanahmed2508]

Love this!

[@asheshmandal4952]

Thank you sir

[@matthewlepage1253]

Thanks!

[@khalolyyan7971]

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

[@ummahyehmmm7403]

That was such a help 😫 thanks sm

[@sagar-uj1nb]

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

[@gabriellagarcia3996]

amazing teacher

[@kavyahegade6477]

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🤝🤝

[@lahiru1k]

Thank you❤

[@user-td1ro3lp4o]

Thank you

[@MOizSUAVE14]

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

[@dylanrobichaud9853]

Thank you!

[@manismanai2276]

Your helped me to pass in my exam.

[@RazorM97]

People who disliked this video have no limits

[@santoshgujar5237]

✨Thank you, Sir, 🙏🌺✨

[@sandman176]

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

[@Gd_Monsterforce]

Making a limit table is satisfying for some reason

[@thestoryofmylifesearchingf9631]

YESS FINALLY I GOT IT THANK U SO MUCH

[@ephremephi2501]

thank you

[@carinamcallister4409]

its time for summer courses again. that means all prof dave all the time

[@MathCuriousity]

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)

[@aminnima6145]

Math is not taught tha way in our school.... They just give the rule and u memorise.... Thank you sir

[@DarinBrownSJDCMath]

11:51 cancelling factors, not terms

[@gaminisiriwardana5946]

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

[@robertwood2424]

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?

[@williamadams137]

6:00, is that the unit step function

[@theteenengineer7589]

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

[@apothe6]

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

[@dariustbt6840]

There are no limits for science jesus!

[@kamalaambika9520]

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

[@MathCuriousity]

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!

[@dakshbadal7522]

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.

[@camellemons3737]

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

[@meltdown6856]

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]

yep!

[@adeboyebamgboye2486]

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!

[@hosinsinaga4694]

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

[@clemsante9048]

I like your videos

[@matamuverner]

prof..... how about accumulation of point?

[@fernandoportal5422]

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

[@ronaldjorgensen6839]

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

[@engnrrmuhammadali7453]

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

[@tGoldenPhoenix]

Done.

[@kontiimanalatit8987]

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)

[@ankitaaarya]

3:00 no one ever told me that, thanks

[@ankitaaarya]

Discontinuity

[@thefact6225]

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

[@Chriss123HD]

you had me at x

[@hansisbrucker813]

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

[@ProfessorDaveExplains]

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

[@hansisbrucker813]

@@ProfessorDaveExplains oooh ok. Thanks

[@kriswillems5661]

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).

[@Jesuisunknown]

My tiny brain is going to expload 😆

[@joschaberg6940]

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]

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

[@erikawwad7653]

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

[@erikawwad7653]

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]

see how this logic cannot be applied for the last 2

[@joschaberg6940]

​@@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: kzbin.info/www/bejne/gZC3dWx9qrVsq7M

[@46-firozc73]

Sir what happens if we get 0/0 instead of - 1/11??pls reply

[@meltdown6856]

0/0 is not a fixed value and is undefined as 0/0 can be 1,2,3 all the way up to infinity as anything multiplied by 0 is 0

[@meltdown6856]

So it's like a void

[@angelisvegan5826]

In plain English.. it's undefined

[@ingvark1968]

I just agree to all the roses below

[@hareecionelson5875]

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)

[@harishgehlot2020]

I am from India 👍🔥☺️

[@benquinney2]

Infinitesimal

[@ahmetselimgurbuz6643]

I wrote it.

[@floweytheflower5261]

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

[@slowfern]

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

[@teekay9498]

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

[@gardenmenuuu]

Great explanations but too short and vague,difficult to catch up due to overloading new words in a short time .please be slow and go thoroughly

[@destinyovbiebo8988]

U wanna learn more?

[@gardenmenuuu]

????

[@sagarshivas298]

Refer a calculus book by stewart

[@adeboyebamgboye2486]

I felt I was the only one seeing it this way. I don't think I got so much out of this particular video

[@peterheath7960]

So, Acillies,DOES beat the tortoise. Nice

[@thisismyname7599]

i know this may sound dumb but couldent you find out what 1/0 is based on this lim x=>0 f(x)=1/x would that not = infinity?

[@shubhamnath8888]

Wtf is wrong with the 10 ppl who disliked????

[@ericpham4011]

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]

What

[@jamesmccreery250]

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

[@eigentlichtoll02]

only watch this for the intro

[@bushbuddyplatypus]

It really doesn't get more boring than this.

[@qualquan]

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]

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]

You just reveled to people that you are dumb

[@brauggithebold7956]

@@ProfessorDaveExplains They're one of Norman J. Wildberger's cultists.