Linear Approximation, Differentials, Tangent Line, Linearization, f(x), dy, dx - Calculus

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This calculus video shows you how to find the linear approximation L(x) of a function f(x) at some point a. The linearization of f(x) is the tangent line function at f(a).
Derivative Applications - Formula Sheet: bit.ly/4eV6r1b
________________________________
Derivatives - Fast Review:
• Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
Local Maximum & Minimum:
• Finding Local Maximum ...
Mean Value Theorem:
• Mean Value Theorem
Concavity & Inflection Points:
• Concavity, Inflection ...
________________________________
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 ...
Marginal Cost & Total Average Cost:
• Marginal Cost and Aver...
__________________________________
Marginal Revenue and Profit:
• Marginal Cost, Margina...
Tangent Line Approximations:
• Finding The Linearizat...
Differentials & Local Linearization:
• Differentials and Deri...
Estimating Function Values:
• Estimating Function Va...
Antiderivatives:
• Antiderivatives
__________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

Опубликовано:

8 окт 2024

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Комментарии : 253

@TheOrganicChemistryTutor 9 месяцев назад

Derivative Applications - Formula Sheet: bit.ly/4eV6r1b Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections

@richphero106 3 года назад

4:18 Find the linearization L(x) of the function a. Use it to estimate f(37) f(x) = x^(1/2) a = 36 8:15 Find the linearization L(x) of the function a. Use it to estimate f(2.1) f(x) = x^(1/3) a = 2 12:10 Estimate the given number using a local linear approximation 8^(1/3) 20:54 Use linearization to approximate ln(1.05) 23:59 Use linearization to approximate tan(46) 30:24 Differentials 36:05 Find the differential of the function y = x^(6) = 7x^(2) +3x 37:35 Find the differential of the function y = x^(2) ln(x) 39:09 Find the differential of the function V = (4/3)πR^(3) 40:36 Find the differential dy and evaluate it using the following values of x and dx 47:56 Graphical representation of differentials 51:11 y = x^(3)-5x+1 and x =2 Δx = 0.1 find dy, Δy

@StefanHFifa 3 года назад

thanks

@coltonmiller872 2 года назад

OMG I didnt even realize it was this long until I saw your comment, life saver here. I was just going to ride it out and really learn lmao

@brycet.9404 Год назад

I love you

@journeytree Год назад

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@bonkezz936 11 месяцев назад

yeah who wants to actually learn @@coltonmiller872

@martinsimbona6145 6 лет назад

In this video,...... Anytime you hear that you know your problems are getting fixed

@CluckYou21 6 лет назад

Exactly, "In this video, I'm gonna show you everything you need to know"

@arknghel9081 5 лет назад

And of course... What? Still searching RU-vid for math help? Are the videos from 2006 reaaaally helping?

@Zephyr-tg9hu 4 года назад

@@lochtlmao Haha got that right

@staticsnipezs1819 3 года назад

lmfao

@af2954 Год назад

@@arknghel9081 hell yea they are, curriculums barely change

@napialex7539 7 лет назад

thank u! for sacrificing your time and make these videos for people! thank u so much!

@lasog7813 5 лет назад

He is getting paid to do it. That's y u see ads on his vids

@abigailjones9868 4 года назад

@@@lasog7813 he is thanking him, because this guy has a passion for the material and gift of illustrating the use of mathematics. Organic Chem Tour guy could be making the big bucks working for oil companies or working in bio-tech.....but, we are grateful he is making these videos.

@Fernando-np9kb Год назад

@@abigailjones9868 not gonna lie, I think monetization on youtube plus patreon is probably paying more than the industry would lmao. still great nonetheless

@pocolocoJOJO Месяц назад

@Fernando-np9kb no lmaoo, the oil industry would pay him way more than ehat he ever made on youtube and also youtube aint a stable job, it could collapse tomorrow, not the oil industry lol

@goddamnedcarrot7045 5 лет назад

It's Thanksgiving, so I just want to say that I'm so thankful for you and your channel. Your videos have helped me so much, and I don't think I would be passing my Calculus or Physics without them. Thank you!

@prodjvenchy 3 года назад

thanksgiving two years in the future and same

@azyle2104 3 года назад

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@anniemonroe9285 2 года назад

its just about thanks giving again and I was thinking the same thing in 2021

@amalabdi714 Год назад

is hoshi your pfp

@manveerkaur8109 11 месяцев назад

thanksgiving two years in the future and same@@prodjvenchy

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wtf

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No he’s mine

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Me before the video: on the verge of tears Me after the video: crying tears of joy

@SK-kn9pl 6 лет назад

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@staticsnipezs1819 3 года назад

Professor Leonard is really good.

@azyle2104 3 года назад

@@staticsnipezs1819 what does he teach ?

@staticsnipezs1819 3 года назад

@@azyle2104 calculus amongst other math subjects

@azyle2104 3 года назад

@@staticsnipezs1819 science too ?

@hugochauschard9516 5 лет назад

organic chem has gotten me through highschool, and now my first semester of university man you're a beast.

@another-learner8677 2 года назад

Thanks for these videos. I use this channel for my Cal 1, Circuits and Chemistry classes. Even though some of the professors are really good at teaching, sometimes it is not enough and you need to find channels like this to help you with your studies. A key take away from this video is Delta X and Y Vs Dx and Dy. From what I understood the deltas are changes in X and Y values of the Function where Dx and Dy are changes in X and Y of tangent line. My professor probably explained this but I did not grasp it until I watched this video.

@adamkumar0 День назад

This man is a big reason why I passed pre-calc, and he is now currently helping me in calc 1.

@jowlenejones 2 года назад

You have no idea how many times you've saved me with Physics and Calculus. Thank you!😁

@albertohuerta 5 лет назад

what kind of cold blooded professor is making you do appx linearization without a calculator :O dude! you're awesome! so detail oriented!

@erenakpnar8361 11 месяцев назад

I have never seen a perfect lesson video on RU-vid like that, Thanks a lot. God bless you

@ВалерийПанков-т5ш Год назад

currently I am studying in Astana IT university, and without your videos studying there would be just impossible. Thank you for providing me with decent quality education.

@jasperjohnson83 3 года назад

You are amazing. I can't thank you enough. You just saved me hours of studying a bulky textbook. Thank you very much and keep up the good work.

@dudeperson7000 7 лет назад

His favorite word is "therefore" haha I love it. Thank you for the video, our professors ripped your cube root 8.1 and put it on our practice questions!

@salomonhernandez2793 7 лет назад

x10 better than my professor. Thank you very much. I learn more in your videos than in class.

@manicsurfing 3 года назад

Thank you so much for making these brother. When I finish my degree and make some money beyond basic ramen I will be contributing towards your generous time spend on these calculus videos. Thanks for being you brother!!! I’m not the only one who thinks this!

@ddahstan6876 2 года назад

Simply put: I feel you. He deserves ounces off of your future promotion. 😉

@pgalatioto 7 лет назад

bro its the small tips you add in that I like the most. Very nice work and thanks for helping me and many others out!

@jasperjohnson83 3 года назад

I read the comments all the time. People are very grateful and the "thank yous" are so many. I think we should take the "thank you" to another level. Do you have a means where we can appreciate you by donating (in appreciation) whatever we please? Once again. Just look at your subscribers (2.8millions). It tells what good work you're doing. Keep it up. Were it not for your videos a lot of people would be in tears.

@bennythejet5026 5 лет назад

i just don't understand how hard it is for a professor to teach these things. Like I am actively participating in class and none of it makes sense but in the first 5 minutes of this video I understand the concept perfectly.

@lajksueye5749 2 года назад

It's the second time you are hearing it so you already have an idea of what you're working with, so this video solidifies things and really helps engrave an understanding of the topics in your mind. On top of that, these videos are mostly explanations of how he does problems and are full of examples, while in class teachers have to cover the conceptual side of things in more detail.

@Starfruit547 5 лет назад

Thank you so much for going over the minuscule algebra. It helps me slow down and process the calculus and get some tips.

@ropi_brian9219 Год назад

This guy is the savior of my AP Chem Gen Chem AP Calc BC AP Physics and Organic Chem career

@thatweirdscienceguy9880 4 года назад

Thank you so much for making these videos. Without them, I'd probably be failing AP Calculus lol

@divineneos4392 4 года назад

1 week left till the exam though :(

@MunaArachnim9606 4 года назад

In calculus, the moment I find out the title of the next lesson, I come and search for his lesson video before the actual lesson so I actually understand it

@prodjvenchy 3 года назад

smart

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@ZNZbane 4 года назад

Shoutouts to this dude for lord willing helping me pass my math final

@candicetang7814 7 лет назад

This is the best and the most comprehensive one! Really helps! Thanks!

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this is literally the 100th time you've helped me out of a hole!!! i can't thank you enough!!! but i'll still try... THANK YOU!!! :)

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@bobjoe164 3 года назад

yeah him and professor Leonard, total gradesavers.

@SamuelScott-p9g 11 месяцев назад

Better explanation than an university professor, well done!

@stephenmiti8829 3 года назад

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I got into ucla because of this guy

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@arjunsampat8683 10 месяцев назад

You have single handedly carried me through university and high school

@micaiahsimmons7245 2 года назад

I give thanks to you. You are literally carrying my calculus grade

@kojicuxt 11 месяцев назад

i'm failing all my classes so i'm really depressed rn. thankfully it's only the midterms and i still can redeem myself in the finals. going to study using your videos bc they help me a lot i hope i pass everything :(

@erenakpnar8361 11 месяцев назад

Dude, I hope you can pass, believe in yourself. Because I passed the midterms for this and other videos.

@kojicuxt 11 месяцев назад

@@erenakpnar8361 thanks, and that's cool. congrats for passing your midterms man

@jaedenk999 11 месяцев назад

how'd u do man

@kojicuxt 11 месяцев назад

@@jaedenk999 i did fine on physics and maths (i passed) but i failed chemistry sadly. just need to study more ig

@jaedenk999 11 месяцев назад

@@kojicuxt at least you passed man, I have to calc final exams this week and I'm at a d right now so this basically determines if I pass or not

@sfundoy5dube59 3 года назад

Thank you, Sir, you are highly appreciated in my life

@rickw3764 Год назад

I like your videos, so thanks for making them. Since this is a video on Linear Approximation, I don't think you have to spend time demonstrating how to do addition or even long division.

@LaibaMatloob-r4c 9 месяцев назад

Preparing for my finals 😢 prayers needed 😊

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i was on the verge of a mental breakdown i love this guy

@nissas1590 5 лет назад

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@josephshaff5194 4 года назад

OH YEAH! Very nicely done on differentials. I enjoyed that.

@sethproaps8899 Год назад

This man's channel needs to be in the national archives.

@thymekey 5 месяцев назад

my dearest love of my life. i got all my exam questions right

@AKINNUGBASORO 11 месяцев назад

i have never watched an hour video before thank you

@Tony-nl6pf 5 лет назад

Watched the whole thing. You sir are a good teacher.

@breannalopez5918 6 лет назад

Thanks wish me luck I’m about to take my calculus exam right now 😭

@ecoplastiny9840 4 года назад

how it did go?

@John-kp1ql 3 года назад

@@ecoplastiny9840 he died

@ecoplastiny9840 3 года назад

@@John-kp1ql that’s all I wanted to hear, thx

@theosproduction8137 Год назад

Just wanted to say: Thank You soo much

@rabiabadar5707 4 года назад

thankyou so much for making these videos as they are really helpful for us, you have been a really great help...may God bless you!

@Lostwolf16 5 лет назад

Thank you so much for existing

@minutechips9414 5 лет назад

I wish he was my profess seems mad excited to teach

@luisnavarro5 4 года назад

anyone watching this during quarantine?

@jackytang5668 4 года назад

hell ya

@boredindeed9685 4 года назад

Yeah... Because I have online classes😂😭

@jadenpatterson3065 4 года назад

@@boredindeed9685 same brotherrrr

@claudiatorok9364 3 года назад

Ohh yeah! We have to if we want to pass

@divineneos4392 4 года назад

Ap calculus in a week fam. Lets get em

@devindepina7660 2 года назад

you are too good. u make calc feel like a breeze.

@aliciapark523 2 года назад

this video is really flawless... beautiful!

@PaolaSocorro21 2 года назад

paying for a calculus course but doing the actual learning in your videos.

@dominicellis1867 Год назад

For the tangent function, you’d still need to use an approximation for pi/90. Could you do a video where you use the Taylor approximation theorem to approximate pi/90 and various other transcendental expressions.

@ШухратРахмонов-ф2ы 3 года назад

ur lessons really healpfull

@sarvarxyz 4 года назад

thank you very much, Organic Chemistry tutor. Can you please add timestamps for long videos?

@potassium6810 3 года назад

what are the conditions on picking what the a is?

@VictoriaSarfo-tl9zz 11 месяцев назад

Sir Please can you do a tutorial on principle of moment, thanks we really appreciate the gold you are giving us 🙏🏽🙏🏽🙏🏽🙏🏽🖐️🖐️🖐️

@ayayoyo6016 Год назад

Bro saved my life in 54 min 😭😭

@justdoit6417 Месяц назад

Ufff simply great 🔥🔥🔥🔥

@ddahstan6876 2 года назад

The reason why I'm here right now is because I find so much motivation in his explanation/ teaching... Might as well call him "God" now because I've never seen one before! 😂 If math can be this good in comparison then I think Lots of folks could have been resuscitated in their career paths had they found him sooner. 😁🤣 Ok. seriously, thank you for all you've done... from a ditzy head.

@happytrails5342 11 месяцев назад

Oh cmon, I dont see anything particularly extraordinary about his videos or teaching method. I've been listening to his videos for years, and the resson they are good, is because they are here. While other channels make the same stuff, but less so extensive. Hes great, but a good teacher in a class? No not really, This type of teaching is monotonous and too consistent to hold attention spans in a classroom. I have been in college for 3 years and have taken a dozen other math classes

@michaelscott6214 4 года назад

Why hasn't this guy start an online college yet!? so much better then Khan

@serajalhorani838 3 года назад

Khan is zero beside this guy

@kaansametguler6258 6 лет назад

this video has clarified a lot for me thanks a lot !!!

@nathanielendick7808 4 года назад

I was so confused during calc today and this video was super helpful. Thank you!

@tannerheiner428 2 года назад

Thank you papi 🙏🏻

@danmiller7649 3 года назад

Good luck to everyone on their calc exams.

@lmy9791 5 лет назад

god bless you. you save lots of life man

@kashevjottaunk979 Год назад

You saved my life

@chidori_channel5849 Год назад

Mr nuttle when you see this, I have been watching him for years

@Super27Jessica 3 года назад

watching this 2 hours before my math final lol

@sumiaaleteer9745 5 лет назад

Thank you sooooo much... You always help me aloooooot I love your vedios alot... Keep going

@gal4743 4 года назад

you sir... ARE AN ANGEL

@khaledalrashidi1 5 лет назад

Thank you so much. You've helped me a lot in different subjects. Keep going!

@Zoraloner 4 года назад

you, sir, are a legend

@VictoriaSarfo-tl9zz 11 месяцев назад

Please please sir I need the topic approximation in binomial theorem and also binomial theorem for positive integral index because without you lam doomed 🤓🤓🤓👍👍👍👍

@ionloghin2172 5 лет назад

20:25 I think you forgot a zero in the L(8.1)=2.0833 while in the long division part it says 2.00833.

@jorgitovitale7735 4 года назад

Ion Loghin no he didn’t forget about it, remember that you multiplied by 10 and 40, so you have to take the comma one spot to the left.

@ProDrTaxi 7 лет назад

You Are The Best !!!!!!

@BhaveeRathod 11 месяцев назад

YOU ARE THE BEST!!!!!!!!

@PHILLYMEDIC69 5 лет назад

thanks dad

@bettypassion5164 5 лет назад

Thanks sooooooooooooo much My calculus lecturer is breaking my neck😢😢😢 Like if you are going through the same agony😂

@TheAbsoluteMost4972 5 лет назад

Same ;-;

@arlanmamytkhan 11 месяцев назад

Thanks, you make more clear about that.😊

@andreasobama9487 2 года назад

Everytime I see math like this, it always makes me wonder who the hell discovered all this and what they must've been smoking at the time.

@lena4431 Год назад

I was a little bit confused about the tan(46) problem, why did you switch from 46 to a radiant, and where did the answer 3 go? so if the 3 is not close to 1.03553, you have to use radiant to get the accurate approximation? Do we have to do that with every problem?

@richardvargas4950 3 года назад

this is where I learn like 80% of my calculus

@mastershooter64 3 года назад

newton and leibniz: wait you don't even invent math on your own? *pathetic*

@mathacademyforall4161 10 месяцев назад

20:25 I think you forgot a zero in the L(8.1)=2.0833 while in the long division part it says 2.00833.

@josepuga381 7 лет назад

YOU ARE THE BEST

@vasistdeo6538 4 года назад

Let 𝑓(𝑥) be a function with the property that 𝑓(𝑢 + 𝑣) = 𝑓(𝑢)𝑓(𝑣) for all 𝑢 and 𝑣, and such that 𝑓(0) = 𝑓′(0) = 1. Show that 𝑓′(𝑥) = 𝑓(𝑥) for all 𝑥 Please help me solving this

@lena4431 Год назад

jeez, they make it sound harder then it actually is, what kind of wording is that???? Is that an approximation problem?

@mikuculus3720 Год назад

e^x

@lucyhuang239 5 лет назад

Really cool, bro! Thx

@brothermason8446 7 лет назад

Why are you so much better than my teacher

@ashwinmurali7647 3 года назад

How did you know to set f(x) to sqrt x for the first one. And f(x) = x^3 for the second one?

@HaleyOrr-m5k 6 месяцев назад

This is probably never going to get answered, but at 22:00 , why is the deriv of ln(1) = to one? I get the 1/x > 1/1 thing, but also when you consider d/dx lnU = U'/U, then ln(1) = 0 bc it's 0/1.

@isaiahpierce7742 4 года назад

You are the GOAT!!!

@esranurgunay1776 3 года назад

Why don't u give a like? u don't even pay for this 1 billion dollar tutorial video...

@fearstraw7 7 месяцев назад

might be years too late but at 20:36 isnt the answer supposed to be 2.00833 because that what you got with the long division but wrote something else.

@superbutter476 3 года назад

Everyone - Calc Teacher: *ew* JG: *god blesssss you*

@KilluaZoldyck-nu4ev 6 месяцев назад

I'm in total tears dad you are such an amazing teacher, you are a the love god bestowed upon us humans, you are an angel, you are magnificient, you are gorgoroyus, you are majestic, you mew everytime and I love when you looksmaxx

@KilluaZoldyck-nu4ev 6 месяцев назад

stfu bro what you even on about

@KilluaZoldyck-nu4ev 6 месяцев назад

Who asked you?

@KilluaZoldyck-nu4ev 6 месяцев назад

I did