❖ Lots of Limit Examples, Part 1 of 6 ❖

[@bennyli4735]

1:00 concludes a 2-hours lecture in 10 seconds, thank you so much

[@carson2889]

I think it's hilarious that I've learned more about limits in the past 10 minutes than I have in over 3 weeks of hour+ long lectures almost every day.

[@jalexsilva8162]

Same

[@thelisaintservant1907]

say that again

[@chesse3547]

i second that lol

[@catherinepangilinan6735]

Im crying you made it so simple and actually gave LOTS of examples so I could try em out myself

[@99BeastMaker]

I just love these types of video where you just mix things up just to give me an idea to expect the unexpected.

[@PM-et6wz]

Brilliant job at this. You make it so clear to understand and make the university teachers look like a joke. Thank you!

[@MatematicaTel]

Pithagorean greetings from Brasil. Thanks a lot for this very good class!!

[@yasmeenzuraik9803]

The most useful video I've watched after watching over 5 videos for limits THANK YOU!!!

[@abbih1135]

Your videos are so helpful- I would not be passing calculus if it weren't for your videos. Thank you for all you do.

[@davidczechowski5468]

more of these short math-related videos are needed. quick review at the start and then some examples, perfect for a prequiz or pretest review when the topic is something that you've studied before but just needed a refresher. thank you!

[@smasher640]

A quicker way to do 3* would be to recognise the denominator as a difference of two squares. 1-x = (1-√x)(1+√x), so you can cancel the 1-√x on the numerator straight away.

[@renewd]

Thanks for the tip. Before Calculus, this technique is not too common, but it is useful in cases like this.

[@cmon9505]

This is exactly what I did

[@Vovkasnya]

Thanks man, your explanation is the best! And your accent is perfect for a foreigner to understand too!

[@wangobango1872]

Midterm @ 6pm. and you are my savior. Thank you

[@sabit619]

My prof is going over limits right now. Had trouble understanding the basics at first, but your videos are making it very easier for me! Actually your 10 min videos make more sense than my prof's 1 hr lectures! Thank you!! Can't wait for the next part. :))

[@kathymckenzie9164]

It was awesome that you took the time to do this immensely comprehensive and helpful limit lesson! Thank you so much, Patrick ~

[@GonBulio]

its a bit crazy how lost i was before I saw this video. the man is going God's work.

[@erinruby930]

I've been watching your videos for 3 years now! You're a life saver!!! Keep it up!

[@Naytastiic]

just started limits in class today going to watch this & more thank you

[@JS-gu7fw]

I have Calculus Exam next week. Talk about perfect timing! Thanks a loooooot!

[@alperyasin710]

How is the results?

[@adamyanam6626]

@@alperyasin710 homie prolly graduated already XD

[@sugaudacity]

I forgot how incredibly helpful your videos are, thank you so much 🙏🏻🙏🏻

[@uibu9652]

that flow chart was a time saver preciate it

[@yugsahu7388]

For number 3, there is a faster and easier solution using the rule (a^2 - b^2) = (a + b) (a - b). The denominator is 1 - x but you can also write it as (a^2 - x^2/2). Therefore , expanding the denominator, you get (1 + x^1/2)(1 - x^1/2). The (1 - x^1/2) cancels out and you get 1/(1 + x^1/2) and you can simply evaluate the limit then by plugging in 1. You will get the same answer, 1/2.

[@Majorstylux1]

Thank you for helping us all out.

[@JPbarbosa8]

Bravo, Bravo. Muito obrigado Patrick pelos exemplos e explicações. Thank you very much Patrick for the exemples and explanations

[@jalexsilva8162]

Tenho que vim em canais gringos pq sinto que 90% deles explicam melhor que meus professores

[@ernestometer]

Well explained. Can't wait for the 2nd part.

[@SilentMover95]

Please release the 2nd,3rd asap! I will be having my exam real soon

[@EverybodyLovesDJ]

You made this make soooo much sense! Thank you!

[@BKKGarrett]

Number 3 seems a bit simpler to me if I factor the denominator using a^2 - b^2 = (a + b)(a - b). So, 1 - x = 1^2 - sqrt(x)^2 = ( 1 + sqrt(x)) (1 - sqrt(x)) ... then the 1 - sqrt(x) cancels top and bottom. Now plug in and you're done.

[@sing1r]

I have a calc exam tomorrow and this is great. Thanks!!

[@GG-dh8ep]

Taking the derivative of 0/0 or infinity/infinity is also another way: way easier too

[@DrLAB123]

Thanks. You are such a good teacher.

[@nicole115920]

i have a college calculus exam tomorrow on limits so thank you so much this was very helpful :)

[@Bennethp]

Here in Belgium we get calculus when you are 17 (life is so unfair)

[@bathsaltzombies8855]

Bennethp lots of people in the united states take calc in highschool, around age 17

[@Bennethp]

Oh really i didnt know, but why do it in uni again ?

[@bathsaltzombies8855]

because you dont get uni credit for highschool calculus unless you pass the AP test, and even if you do pass the AP test, many people still have to take higher levels of calculus as a requirement in their major.

[@Bennethp]

Oh didn't know thank you for clarifying :)

[@leeannholguin]

Thank you so much for posting videos! I love you!

[@harlbertmayerh7523]

I likeeeeeeeeeeeeeeee someone that writing with left hand its so satisfying !!!!!

[@TheLukey151]

thank you so much man, seriously this helped me so much

[@SvenKubitzMedia]

English explanations of mathematical issues really help me get certain techniques better than actually German tutorials as it would be common for me as a native German :D

[@illynameli]

I feel exactly the same. I am a Portuguese native, but i learn a lot better when sth is explained in English

[@stormgaming2784]

same here with french

[@faroukahmed5102]

the same with Arabic native speaker...

[@anderswallmark9787]

Don't forget that you can also use L'Hôpital's rule for indeterminate form!

[@gibsonj338]

Anders Wallmark I was just going to say the same thing. I worked that out and came up with the same answer.

[@justinwu136]

the flow chart is so helpful!

[@ednimenzo1984]

I love this channel. Keep it up PatrickJMT.

[@jacobh1995]

Thanks! I'm doing limits in college calculus right now.

[@РусскийПатриотЯша]

Isn't it wonderful? paying uni fees so that people like this guy explain me math.

[@patrickjmt]

send me your tuition

[@РусскийПатриотЯша]

@@patrickjmt If uni wasn't the mafia but legal, I would've T-T

[@LuciaAzanedo]

This was such a helpful video! Thank you for explaining everything very well!

[@patrickjmt]

glad it helped :)

[@mathssolutions3635]

For the last example, lim x tending to 0 could have worked perfectly without having to change to 1. Then the root of 1 is +1 or -1. I suppose you should have showed both the workings instead of assuming directly that √1=1. So far, well done.

[@weddesudesu6119]

Great help 'coz our midterm's just around the corner.

[@geoycs]

I’m enjoying your video with popcorn and Heineken.

[@patrickjmt]

that sounds like a nice way to enjoy it :)

[@vongsothea413]

Great! Now I can escape the sad kappa personality that been bothering me when I was dumb.

[@patrickjmt]

lol

[@bantlmasaayaklar7994]

Hey mate, firstly thx for this video and the secondly, the question at the last of the part, u could make it short way u know. (I ll use this sembol / as a square root) 1-x equal (1-/x).(1+/x) from the difference of two squares after that 1-/xs take each other away, 1÷1+/1 equal 1÷2. It s shorter, we could gain time a little bit :). Peace from Turkey!

[@shahadas907]

You are my hero, THANK YOOOU SO MUCH !!

[@TheGuitarNewby]

mate, you are really well educated in mathematics... damn!

[@seppe8156]

Problem 3)* you can also write 1-x=(1-sqrt(x))*(1+sqrt(x)) using a^2-b^2=(a-b)*(a+b)

[@gaurav8998]

does anyone notice he is lefty ps: u explain very good

[@godwinekojah-wf8im]

Limit problem is exciting

[@stevennerheim3739]

Thanks man your video was life changing

[@tokitomuichiro735]

Thank You So Much!!! Really helpful

[@hsbshbd-sh7797]

Thank you so much for this! I'm taking calc right now and this helped a lot!

[@tayyab.sheikh]

Exceptionally great 👍🏽

[@ferdinandchizema7445]

Thanks a lot, i appreaciate your work. it helps a lot.

[@celesteadeanes4478]

Patrick, how about multiplying by the denominator ‘s conjugate in number 3? Instead of the numerator? I thought clearing there more important. I tried it you get a zero in the denominator. I guess you should exhaust both possibilities?

[@harshaddave857]

Very very fascinating!!!!!

[@divygoal8504]

THANK YOU! BIO CALCULUS TEST IN FEW HOURS!

[@patrickjmt]

good luck!

[@hassanfalah1033]

very gooooood👍👍👍👍 I Love Math.

[@darkzooro531]

وهوة هم يحبك ههههههه

[@hassanfalah1033]

+jaes loker ..هههههه

[@chankelly4964]

very helpful and detailed video. Thank you !

[@tb2748]

For number 3, I graphed the rational function in desmos and found that there is no "left hand" limit for this particular problem. Which would imply that the limit doesn't exist? Why does this limit equal 1? Brand new calc student here so I have no clue what I'm doing, so correct me if I'm wrong about anything.

[@bantlmasaayaklar7994]

There is critic point. When u see 0÷0, x÷0 then u must reduce somethings for find to answer. Hope u understand me

[@b-rad6978]

This is awesome !

[@b3nythomas284]

U are a life saver

[@jonykhan4395]

Good work, Does limit solve undefined or indeterminate form types of problems or both ? For instance if a function is undefined 0/0 or indeterminate 1/0 Then can limit be appllied on both bases? Another point is that Do we use limits to determine the y-output where the ACTUAL FUNCITON was unable to determine the y-output? Could we say that both function formula and limit formula ARE NOT SAME? Why we say a function is undefined at a specific x value?? A function is a function when all of its domain members have unique images BUT at a specific x value the function does not have image so its not a function anymore because it is not following the definition of a function.

[@sweethartia]

Extremely helpful thank you so much

[@patrickjmt]

you are very welcome :)

[@rfmvoers]

In your original question 3, x cannot approach 0 from the left, so the (two-sided) limit does not exist.

[@rfmvoers]

I'm enjoying the series by the way.

[@faizanm1563]

What an mad lad

[@jenishere617]

So clear thank you!

[@FriesKhan]

Dude ur amazing

[@degraj418]

this is amazing thanks

[@patrickjmt]

No problem!

[@ElifArslan-l9g]

thank you

[@syedmehranshah718]

Thnk you so much

[@avestaabdulrahman6549]

quite helpful

[@1230-o6r]

This video was helpful

[@maryph4255]

This is very helpful

[@raedrid2499]

Nice one keep doing that please

[@Cjharps2442]

This sharpie scraping the paper make it hard to listen to, good thing for captions

[@ypn.official]

Flip & Multiply .

[@icecubegaming3661]

in the 3* example can't we use a²-b² identity?

[@oliviawang3558]

soooooo great!

[@sabek7112]

so helpful

[@matiassantacruz5487]

You are my God!!!

[@KeyurKumbhare]

In the 3rd problem, what would be the solution if x is tending to 1- ? In there any difference between the two?

[@frondescenceful]

I don't really get why you had to do that with 3* and do the limit x -> 1+ ... Doesn't that change the original problem?

[@hearvie]

With conjugate don't you rather use the denominator and just change the operation?

[@driftlord9447]

thx u solved my problem

[@annacristinapozzato1860]

Hi thanks for your videos. I have a question when solfing a limit I get the form k/0 why do i have to determin if the limit is equal to plus minus infinity or if it doesn't exist? I believe that it always doesn't exeist because it doesn't approach any number and k/0 is always either plus or minus infinity. Sorry I do not understand. Thanks for your time. Anna

[@akb4895]

for number 2, why it's not 0/0?? And when do we know it's 0/0 or we have to factor????

[@EhKurd]

thank u friend

[@qqmayakashi]

Is rationalization and conjugate different?, when does the sign do not change when conjugated?

[@Rumasila]

Thank you Thank you Thank you x100000 haha :D Really needed this!

[@aaronwong7088]

why no just use l'hopital 's rule for everything ?

[@stacy-ann1722]

In the last question, why after getting one you continued? Would it be incorrect to leave it at 1? Please explain in another way than you did in the video. Thanks in advance.

[@eliasregehr7756]

1 is correct for 3) but this Problem was too easy so he made a new more difficult variation of this task were it is not so obvious.

[@Funny_Text3]

I love you mann

[@Owsj4]

For the third problem, does the left-handed limit exist?

[@bestnocture]

Owsj4 nope.. but the limit does exist since the function is continuous, so you can find it by lim x->0+

[@Mrius86]

Did you check your phone at 10:49?

[@maryph4255]

12:29

[@aleona7965]

What if there is no 'as x approaches to sumthing'??

[@hearvie]

How do you know when it's undefined?

[@abcforgt]

Valeu!