L'hopital's rule

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  • เผยแพร่เมื่อ 4 มี.ค. 2018
  • This calculus video tutorial provides a basic introduction into l'hopital's rule. It explains how to use l'hopitals rule to evaluate limits with trig functions, fractions, exponential functions with e^x and natural log functions such as ln(x). To use l'hopital's rule, you need to take the derivative of the numerator and denominator of the fraction any time you have an indeterminate form as a result of direct substitution.
    Full-Length Math & Science Videos:
    / collections
    ___________________________________
    Introduction to Limits:
    • Calculus 1 - Introduct...
    Derivatives - Fast Review:
    • Calculus 1 - Derivatives
    Introduction to Related Rates:
    • Introduction to Relate...
    _____________________________
    Extreme Value Theorem:
    • Extreme Value Theorem
    Finding Critical Numbers:
    • Finding Critical Numbers
    Local Maximum & Minimum:
    • Finding Local Maximum ...
    Absolute Extrema:
    • Finding Absolute Maxim...
    Rolle's Theorem:
    • Rolle's Theorem
    ________________________________
    Mean Value Theorem:
    • Mean Value Theorem
    Increasing and Decreasing Functions:
    • Increasing and Decreas...
    First Derivative Test:
    • First Derivative Test
    Concavity & Inflection Points:
    • Concavity, Inflection ...
    Second Derivative Test:
    • Second Derivative Test
    _________________________________
    L'Hopital's Rule:
    • L'hopital's rule
    Curve Sketching With Derivatives:
    • Curve Sketching - Grap...
    Newton's Method:
    • Newton's Method
    Optimization Problems:
    • Optimization Problems ...
    _______________________________________
    Final Exams and Video Playlists:
    www.video-tutor.net/

ความคิดเห็น • 604

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  ปีที่แล้ว +41

    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
    Next Video: th-cam.com/video/JTVNUdL7sWs/w-d-xo.html

  • @ardor2457
    @ardor2457 4 ปีที่แล้ว +4962

    The moment you hear his voice, you know you're in the right place

  • @zeroc977
    @zeroc977 3 ปีที่แล้ว +531

    Dang, this is easy. My math teacher made it seem a hell lot more complicated. If everyone could teach like you, the world would be a better place.

    • @baltazarsolorzano-chiarizi7372
      @baltazarsolorzano-chiarizi7372 3 ปีที่แล้ว +40

      My god... Human progress would increase exponentially.

    • @ashcraft257
      @ashcraft257 หลายเดือนก่อน

      It isn’t but I just can't seem to think, I have a test tomorrow.

  • @sadabhafiz5239
    @sadabhafiz5239 4 ปีที่แล้ว +949

    "anything raised to the power 0 is 1"
    Infinity^0: "Am I a joke to you?"

    • @joshscores3360
      @joshscores3360 4 ปีที่แล้ว +35

      0^0

    • @sadabhafiz5239
      @sadabhafiz5239 4 ปีที่แล้ว +35

      @@joshscores3360 it's actually 1 lmao

    • @Sea_bear_42
      @Sea_bear_42 4 ปีที่แล้ว +86

      Sadab Hafiz no it’s not. It’s actually approaching one, but will never really get there, like an exponential equation

    • @pratikdhakal8241
      @pratikdhakal8241 4 ปีที่แล้ว +66

      @@Sea_bear_42 just like your crush's love for you!😂
      LMAO!

    • @Sea_bear_42
      @Sea_bear_42 4 ปีที่แล้ว +102

      Pratik Dhakal what a sorry excuse for a joke

  • @saugatshrestha5272
    @saugatshrestha5272 3 ปีที่แล้ว +358

    Me and my homies were going like
    "L Hospital"
    Damn my whole life was a lie.

    • @Arthur-qe8xc
      @Arthur-qe8xc 2 ปีที่แล้ว +22

      Le Hospital

    • @cyphexal1162
      @cyphexal1162 2 ปีที่แล้ว

      It's also called l hospital rule..

    • @briabree7683
      @briabree7683 2 ปีที่แล้ว +7

      @@cyphexal1162 there is no "s" in the spelling of L'Hopital...

    • @asdfghjklzxcvbnm3166
      @asdfghjklzxcvbnm3166 2 ปีที่แล้ว +1

      Bria Bree there are two spellings...

    • @briabree7683
      @briabree7683 2 ปีที่แล้ว +1

      @@asdfghjklzxcvbnm3166 you okay?

  • @ahanamohammed1541
    @ahanamohammed1541 3 ปีที่แล้ว +626

    Why can't all professors be like you lol. Your a lot more reliable than most sources I could compare

    • @XVII12
      @XVII12 2 ปีที่แล้ว +17

      Why Cant the exams come as easy as his explanation too...

    • @chipiegg1466
      @chipiegg1466 ปีที่แล้ว +21

      @@XVII12 because exams don't test knowledge, they want to hit a certain average mark with exams, in order to do that, they need to add questions most people would not be able to solve for example because its a bit unfamiliar

  • @13PieceBucket
    @13PieceBucket 4 ปีที่แล้ว +390

    I have no idea how I would get by without your tutorials. You are a blessing to students everywhere, stay great.

  • @anilguneri8224
    @anilguneri8224 5 ปีที่แล้ว +452

    i have 90 minutes to midterm exam and you are perfect :)

    • @riyajain3404
      @riyajain3404 3 ปีที่แล้ว +30

      You done with your degree yet or not? xD

    • @slolilols
      @slolilols 3 ปีที่แล้ว +3

      Lmao

    • @ud2181
      @ud2181 3 ปีที่แล้ว +27

      I'm his teacher he got F-, so yes he dropped out of school

    • @slolilols
      @slolilols 3 ปีที่แล้ว

      @@ud2181 lool

    • @StephanieQuiroz-ps9nl
      @StephanieQuiroz-ps9nl 2 ปีที่แล้ว +14

      got my last midterm in 50 minutes havent done any class work in one month bc i am depressed :D

  • @jesseandrade9589
    @jesseandrade9589 4 ปีที่แล้ว +726

    bruh, why can't all professors just teach comprehensively like this.

    • @miguelconfesor4701
      @miguelconfesor4701 4 ปีที่แล้ว +89

      because education is designed to fail students.

    • @fatima7174
      @fatima7174 3 ปีที่แล้ว +44

      @be happy We literally pay them 1500+ for one course per one-semester and what do they do? They took advantage of the pandemic and squeezed us in one class (1123 students) over zoom. Multiply $1500 by the number of students they can't afford to bring in another professor or make the lesson longer?🙄 They're pity.

    • @jonahnichols2158
      @jonahnichols2158 3 ปีที่แล้ว +15

      @@fatima7174 Profs don't get paid shit. That money goes to the university.

    • @mercury2632
      @mercury2632 3 ปีที่แล้ว +7

      @@fatima7174 they squeezed 1123 of you into one call????? holy shit!

    • @fatima7174
      @fatima7174 3 ปีที่แล้ว +3

      @@mercury2632 yes it was stressful but thankfully I've gotten through it

  • @isaacliu._.6899
    @isaacliu._.6899 3 ปีที่แล้ว +93

    I have not felt this excited about learning something in math in years. Went from not even knowing how to pronounce L'Hopital to knowing how to do all the problems by myself. Thanks a bunch!

  • @CHAOS80120
    @CHAOS80120 4 ปีที่แล้ว +141

    His voice is so calming and beautiful

  • @obscure_genesis
    @obscure_genesis ปีที่แล้ว +41

    His explanations and examples are like the perfect mix of in-depth and easy to digest. Great video

  • @benjamintraudcampos2828
    @benjamintraudcampos2828 5 ปีที่แล้ว +237

    u r a gift from god

  • @ImVeryWholesome
    @ImVeryWholesome ปีที่แล้ว +20

    I usually panic when I study and try math problems, but this guy makes it feel so welcoming and easy to understand

  • @wahidnoori2259
    @wahidnoori2259 5 ปีที่แล้ว +131

    Oh my God! before watching this video every thing looked very hard to me when it was coming to L'hpitals's rule. This is great teaching. very clear and makes calculus easy to understand. Thanks.

    • @tcritt
      @tcritt 4 ปีที่แล้ว +9

      It may be because this video doesn't teach you the "why", which is what your teacher is probably trying to teach you, but rather how to plug and chug your way through an exam.

    • @PedroTechnologies
      @PedroTechnologies 4 ปีที่แล้ว

      @@tcritt This is the best explanation I have seen to why this youtube tutorials always seem so much better than the class. But then again, if the class is meant to teach us the why, then why does the test ask us to plug stuff in.

    • @tcritt
      @tcritt 4 ปีที่แล้ว +3

      @@PedroTechnologies If you know the why, you are more likely to get the trickier questions right. Those questions are the ones where it's not immediately obvious what formula is required and where you need a flash of insight to even know where to begin. It all depends on the level, objectives and rigour of the course.

  • @daddy_myers
    @daddy_myers 2 ปีที่แล้ว +19

    L'Hopital's rule is honestly such a powerful tool; it saves so much time by sparing all the factoring work in polynomial limits and makes your life a helluva alot easier!

  • @rondavis236
    @rondavis236 ปีที่แล้ว +30

    What an amazing class sir , you are the best teacher i have ever seen

  • @huh.2
    @huh.2 4 ปีที่แล้ว +6

    This helped me SO MUCH, my professor started with explaining l’hôpital’s rule and THEN started showing how to use it, which made me so confused, but now I really get how to use it, thank you!

  • @mikedrewson5545
    @mikedrewson5545 6 หลายเดือนก่อน

    I only discovered your channel last night but thank you so much. I initially was using Khan academy for studying for a test later today but my dad found your channel. At first I wasn’t interested, but when I watched your videos, I was shocked. They were easy to understand and in depth. I’m so glad my dad found your channel. May God bless you.

  • @Traivss
    @Traivss 6 หลายเดือนก่อน +5

    man I don't know if you read comments on these old videos but I just wanna say thanks, literally every question I have for any of my recent classes that I google one of your videos comes up. They're succinct, well worded and easy to understand. You rock.

  • @vineethvenugopal8613
    @vineethvenugopal8613 ปีที่แล้ว +7

    Thank you very much man. Today i just viewed this content 10 minutes before my exam and I was able to answer the questions easily. You are legend ❤❤

  • @smellymewi
    @smellymewi 4 ปีที่แล้ว +2

    I cant believe how simple your approach is. My lecturer goes all over the place for 2 hours+ and yet, I dont understand shit. Whereas I watched your video and I understand how to approach questions using the L'hopital rule. Thank you so much

  • @crackette6709
    @crackette6709 2 ปีที่แล้ว +4

    As a senior in college who waited way too long to finally take calculus, you are my hero and I worship at the shrine of your knowledge

  • @somokik.m7138
    @somokik.m7138 5 ปีที่แล้ว +6

    to be honest i didn't know 0/0 it can be solved to give a reasonable answer...Sir u made it clear now....you just proved that a scientific calculator is programmed because it says 0/0 its an error...L'hopital rule its now simpler to me....keep helping for those who are weak in maths,chem,physics,stats,etc you are doing great work...

  • @axtas
    @axtas 2 ปีที่แล้ว +12

    I want you to know, I don't go to my normal Calculus class anymore because my prof talks too fast and complicates things. Instead, I watch your videos and take notes on your content instead. I'm getting higher grades than a lot of my peers. You should be very proud of this.

    • @6kbps
      @6kbps ปีที่แล้ว +2

      i wish i didnt have to waste 3hrs each day, twice a week showing up just to have it go back to yt

    • @axtas
      @axtas ปีที่แล้ว +1

      @@6kbps no fr, i got a 98 on my final and all from reviewing from this channel

  • @hakarali6289
    @hakarali6289 5 ปีที่แล้ว +30

    Thank you so much you saved my life more than One thousand times.
    Hope you keep continue from publishing These Kinda useful mathematical explanations
    Just to tell you ,you are my dependent teacher, thanks again

  • @meghanmilosevska7447
    @meghanmilosevska7447 4 ปีที่แล้ว +4

    having my first exam of Mathematics 1 this week, you are saving my life

  • @georgesadler7830
    @georgesadler7830 ปีที่แล้ว +2

    MR. Organic Chemistry Tutor, thank you for explaining L'hopital's Rules with solid worked out examples from start to finish. Pattern recognition also helps with understanding L'hopital's Rules in Calculus Two. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.

  • @aky495
    @aky495 3 ปีที่แล้ว +2

    OH MY thank you SO much!! i have my calculus exam in 2 hours and you saved me cuz i had found this rule to confusing but no more now!! PS. your voice is so calm and gentle I LOVE IT

  • @kindak.c.5778
    @kindak.c.5778 5 ปีที่แล้ว +154

    I'd be failing AP Calc if it weren't for you 😭❤️

    • @davidmorales2859
      @davidmorales2859 4 ปีที่แล้ว +3

      Kinda K.C. Ab Or Bc

    • @Punicia
      @Punicia 2 ปีที่แล้ว

      @@davidmorales2859 Cd

    • @vineet4883
      @vineet4883 2 ปีที่แล้ว

      Hey I am from India and I want to know in which University do you go

  • @daniayakdi9874
    @daniayakdi9874 4 ปีที่แล้ว +7

    I totally love your voice when you teach, I guess that I felt in love with calculus just cause of you

  • @augustine1199
    @augustine1199 2 ปีที่แล้ว

    This topic had been haunting me since the start of my class and I have exams three days later and now I can say I aced this topic all thanks to you 😭
    Thanks for helping me be a little confident in this topic

  • @LowVizGaming
    @LowVizGaming 4 ปีที่แล้ว +15

    THAT'S SO BUSTED!!!! I'm getting ready to take Calc 3 and I literally had never appreciated L'hopital's rule before now. Game changing. Thanks so much for this video!

    • @happytrails5342
      @happytrails5342 5 หลายเดือนก่อน

      dog, I'm concluding calc 1 and seeing this....how did you make it without it! LOL

    • @4fgaming925
      @4fgaming925 24 วันที่ผ่านมา +1

      @@happytrails5342 me in class 11 seeing this lol

    • @happytrails5342
      @happytrails5342 24 วันที่ผ่านมา

      @@4fgaming925 lol! Best of luck in finals

    • @4fgaming925
      @4fgaming925 24 วันที่ผ่านมา

      @@happytrails5342 actually in my country the session starts in April so I just joined grade 11, its not been more than a month, thank you tho

  • @themandan9456
    @themandan9456 7 หลายเดือนก่อน +4

    I just learned a lecture’s worth of teaching in 5 minutes.

  • @namiadel6919
    @namiadel6919 3 ปีที่แล้ว +1

    You are the best teacher in math in my whole life

  • @unclelelax8341
    @unclelelax8341 3 ปีที่แล้ว +5

    A huge shout out to my professor who did not even teach us one time since our online classes and give these kind of Calculus 1 problems.🙃 Thanks OCT for being the best teacher💖

  • @MustafaAhmed_99
    @MustafaAhmed_99 6 หลายเดือนก่อน +2

    Thx buddy could u believe I’m studying electrical and electronics engineering and I’m from iraq and u are helping me out I’m very grateful ❤❤

  • @BallTribeTV
    @BallTribeTV 3 ปีที่แล้ว +3

    This video helps me a lot for AP Calc AB! Thank you!

  • @diemngo8451
    @diemngo8451 3 ปีที่แล้ว +15

    this 13 minute video is so much easier to understand than my prof's 40 minute lectures

  • @HelloWorld_88
    @HelloWorld_88 9 หลายเดือนก่อน +2

    Bro, You deserve a Noble prize.

  • @Aaron-gx9gv
    @Aaron-gx9gv 2 ปีที่แล้ว

    My favorite tutor for over 4 years

  • @christopherramsey6001
    @christopherramsey6001 ปีที่แล้ว +2

    An excellent explanation of L'Hopital's Rule. I really learned a lot !

  • @prawinkumarsingh8287
    @prawinkumarsingh8287 6 ปีที่แล้ว +44

    Fantastic teaching!!!

  • @harmevers2661
    @harmevers2661 2 หลายเดือนก่อน

    This bro solved all my calculus frustration with excelent explaining skills and a calm voice, if only he was my teacher

  • @alliswell8376
    @alliswell8376 4 ปีที่แล้ว

    Simple n clear explanations , thanks from the bottom of my heart Sir

  • @hope2071
    @hope2071 ปีที่แล้ว

    your voice make my heart calm and give me a stable energy to love studying Mathematics. Thank you sir.

  • @kennymalatji4583
    @kennymalatji4583 11 หลายเดือนก่อน

    The only online tutor that matters in the world

  • @laithdarras6389
    @laithdarras6389 ปีที่แล้ว +1

    This guy is singlehandedly saving my calculus grade

  • @Magnetshroom
    @Magnetshroom ปีที่แล้ว

    This prof teaches us with a precise details.

  • @highsocietyfella6165
    @highsocietyfella6165 2 ปีที่แล้ว +1

    Super helpful and straightforward, thank you very much!!

  • @iwillnevershower
    @iwillnevershower ปีที่แล้ว

    my teacher is as good as you thankfully but a revision is always great.
    but ive been to the position where the teacher turned basic calculus to rocket science for absolutely no reason
    and this is free whereas universities cost fortunes, organic chemistry tutor thank you i love you

  • @Chaosdude341
    @Chaosdude341 3 ปีที่แล้ว +1

    You the man, man. Thanks for these excellent resources.

  • @deisymutesi1966
    @deisymutesi1966 8 หลายเดือนก่อน +1

    Really grateful for your help with my academics, big up man

  • @Green_Peas9999
    @Green_Peas9999 5 ปีที่แล้ว +7

    Thanks for the explanation! It helped a lot since I came into these "indeterminate" limits questions. I didn't know how to answer them before

    • @Joshua-fq9tm
      @Joshua-fq9tm 4 ปีที่แล้ว

      ebo gago ginagawa mo dito hahahaha

  • @brandondavidwalker4809
    @brandondavidwalker4809 หลายเดือนก่อน

    bro is so wicked in how he knows everything. i wish i was half as dedicated as this guy

  • @joanantinda887
    @joanantinda887 2 ปีที่แล้ว

    This video really helps me to understand the limits more.

  • @EthanPricco
    @EthanPricco ปีที่แล้ว +1

    I learned more from this 13-minute video than I did from my 1-hour lecture about L'Hopital's Rule.

  • @Itsmagalie_
    @Itsmagalie_ 5 ปีที่แล้ว +24

    Incroyable ! Merci beaucoup

  • @YML
    @YML 7 หลายเดือนก่อน +1

    It's amazing, there's not a single sentence of nonsense in the entire video, it's brief and powerful!

  • @malibuinsane
    @malibuinsane ปีที่แล้ว +1

    I just got the highest grades because of u ! Thank u so much i don’t know what could i do without u😢❤️

  • @pfeliciano4062
    @pfeliciano4062 5 ปีที่แล้ว +53

    You are literally fire. I can’t even... 💍

  • @reygemarlarong5686
    @reygemarlarong5686 3 ปีที่แล้ว

    Good luck for my midterm today.
    Thank you for this! 😊🧡

  • @bradleyh614
    @bradleyh614 3 ปีที่แล้ว

    GOAT you got me through organic and all types of math

  • @Black_heartttttt
    @Black_heartttttt 5 วันที่ผ่านมา +1

    You’re a hero and you are a legend 🖤

  • @iliketurtles7067
    @iliketurtles7067 2 ปีที่แล้ว +2

    I have learned more in 13 minutes than in the 5 two hour lectures that I have had

  • @kpoli7494
    @kpoli7494 ปีที่แล้ว

    Thank you so much sir. Your each and every video is so helpful for many student like me. lots of love from Nepal.

  • @syabongajele6431
    @syabongajele6431 4 ปีที่แล้ว

    I RATE YOU IN THE TOP 20 OF MATHS GURU WORLDWIDE,THANK YOU

  • @abdullaharif1270
    @abdullaharif1270 ปีที่แล้ว +1

    My University paper is just after 3 Hours and I am watching this video now 😅😂.
    Thanks Sir Allot. ❤
    Lots of love form Pakistan ❤

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    @t-izzieleamsi8722 ปีที่แล้ว

    I salute you. Best tutor ever🖐️🖐️

  • @sofiavizcaya6060
    @sofiavizcaya6060 5 ปีที่แล้ว +1

    Thank you. I loved your explanation.

  • @JamesBrodski
    @JamesBrodski ปีที่แล้ว

    What a great video. Thank you so much for making it!

  • @nikosdallas6149
    @nikosdallas6149 4 ปีที่แล้ว +1

    U soo good Man U must be the best teacher keep it up

  • @richards_greatman
    @richards_greatman 2 ปีที่แล้ว

    And again I'm right here at the centre of knowledge. How else can one say 'Thank you'?. Thank you Prof.

  • @ayushvaidya6608
    @ayushvaidya6608 3 ปีที่แล้ว +41

    " If you multiply a large number by a large number, you get an even larger number!! " - OChem Tutor 2018

  • @tshepangratlhako9037
    @tshepangratlhako9037 4 ปีที่แล้ว +1

    I am getting this degree because of you, thank you

  • @muspanisho
    @muspanisho 3 ปีที่แล้ว

    Very clear explanation, Thank you so much

  • @wyattnelson7574
    @wyattnelson7574 2 ปีที่แล้ว

    Literally teaches better than any teacher I’ve had in college

  • @AliceBabiii
    @AliceBabiii 5 ปีที่แล้ว +1

    Thank you so much! U saved my degree TT

  • @helenemso32
    @helenemso32 4 หลายเดือนก่อน +1

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  • @jasminejones7922
    @jasminejones7922 2 ปีที่แล้ว

    Explained perfectly! Thank you

  • @eira2712
    @eira2712 5 หลายเดือนก่อน

    I felt so stupid when I didn't understand this in my class, thank u so much for explaining it so beautifully, you are a superhero.

  • @aed1995
    @aed1995 2 ปีที่แล้ว

    Thank you very much for this wonderful explanation. Unfortunately I used your method ( 10:31 / 12: 39) in my last exam but my teacher said you can't do this method because is not existed... because he never seen it before 😂and he asked me to give him a proof that it's correct... thank you again for your help

  • @riffster
    @riffster 3 ปีที่แล้ว

    This guy sounds cool and is super smart and using TH-cam to help us 👊🏽 much oblige man God bless

  • @markwagdyel-magrisy6620
    @markwagdyel-magrisy6620 2 ปีที่แล้ว

    Watching from Egypt for my grade 12 calculus exam!!

  • @fuadqasimov2456
    @fuadqasimov2456 ปีที่แล้ว

    i wish we had professors like you

  • @gilliangilliangillian
    @gilliangilliangillian 5 ปีที่แล้ว +1

    duuuuuuuude my teacher's out sick today and you saved my butt on my homework

  • @mahmoudezzat5460
    @mahmoudezzat5460 3 ปีที่แล้ว

    idonno why i feel comfortable when i hear ur voice

  • @basheerhijaz8392
    @basheerhijaz8392 3 ปีที่แล้ว

    Best tutor ever!!!!

  • @ayae1290
    @ayae1290 2 ปีที่แล้ว

    Thank you so much. You really helped me. I hope you contiue your good work.

  • @BNguyen-cy1ub
    @BNguyen-cy1ub ปีที่แล้ว +1

    you have save my life sir

  • @ninegames4568
    @ninegames4568 4 ปีที่แล้ว +4

    This is like the ultimate weapon to tackle Lim problems...

  • @dossube
    @dossube 2 ปีที่แล้ว

    These 13 mins is greater than the 13 years I have learned calculus lmao. Gracias, thank you, merhci.

  • @neilkwishu4097
    @neilkwishu4097 7 หลายเดือนก่อน

    This man is just perfect

  • @naftalynyaga1653
    @naftalynyaga1653 4 ปีที่แล้ว +1

    Thanks man ...this is so good from kenya @ technical university of mombasa

  • @ughmina
    @ughmina 4 ปีที่แล้ว +2

    bless you!! actual life saver

  • @leonardorantes9193
    @leonardorantes9193 2 ปีที่แล้ว

    your voice calms me

  • @KPOPGuru1
    @KPOPGuru1 5 ปีที่แล้ว +2

    THANK YOU JUD KAAYO DO KAY MAAYO KAAYO KA MUTUDLO. THANK YOU! THANK YOU! THANK YOU!!!

  • @KaaBockMehr
    @KaaBockMehr 4 ปีที่แล้ว +1

    Thanks a lot for this good presentation :)

  • @jen5sentrypl1
    @jen5sentrypl1 5 ปีที่แล้ว +3

    bless now maybe i won’t fail my calc final 🥰

  • @dawndong1846
    @dawndong1846 ปีที่แล้ว

    So easy to understand, thank you!!!!!!!!