His teaching is amazing. However, what's really amazing is the fact that he can answer a person's question so well. It's actually quite easy(for me), to give good presentations/teachings, but what actually makes it difficult, is when they ask questions! It'll take me time to understand and think of the best way to actually solve the person's question, without confusing them even further. However, Mr.Woo barely hesitated before he understood, and solved the problem. Great respect for that.
What really got me into math was one day in my first Calculus class, my teacher who reminds me am lot of Eddie, let me go on for about 5 minutes working things out in my head as to WHY the derivative is what it is and not just "what is it" and he let me figure out it's real world application and meaning myself, and all of the sudden everything we had been learning about was REAL, not just something I was being told. And then my teacher said "I can't believe you just backward logic'd yourself into finding out what a derivative is. Well done." And everything was just so joyous.
Thanks Eddie. I am a 68 yo and just refreshing my maths, with your help (because I can). When I was at school, in the 60's, my maths understanding was greatly elevated by understand the application ( to the real world) of the math being taught at the time. One application was logarithms. It was to explain the phenomena of the world around us, in one case about sound, and to calculate the compression of air when sound travels, is a log expression. It is likely that at each step, in your explanation, you would suggest where this math method would apply in the real world. The application of math, has given me great benefit, as I was fully engaged, and could see the meaning of math, and to see it being important for my future.
That's a wonderful take on Math. I'm majoring in Mathematics and sometimes struggle to see the significance of the contents I'm taught because they seem too abstract. Anyway, I hooe you're doing well.
Hi sir, I am Aditya soni from India I am impressed by your courage and love for maths, and I want a little bit help from you. I am studying maths but I don't know how can we apply it in the real world. if you will suggest something for the resources from where i can learn the application of maths, it will help me a lot,, Hoping for a positive response from you.
@@nicoles_handle it's not hard at all. This is a very common practice in Australian schools where he is at. Year 11 curriculum is the introduction with first principles and an explanation of how to get it Year 12 you should know how calculus works well enough to be able to simply apply rules. Trigonometric calculus as well as logarithmic calculus is not taught until Year 12 when the students should have a good knowledge of how and why calculus is what it is.
@@swordiexd i was more talking about how hard it is to convey something so abstract, and how he makes it look easy. i get foundation, but his teaching is approachable.
If I had had you as my math teacher in high school or college many years ago everything would have been so much easier. Why did I never get the explanation of why the derivative is what it is, but instead only got the final result to be accepted as gospel? These series of videos is just great, as the rest of yours that I have watched. Thanks a lot for doing this!!
When I learnt this at my high school, the teacher was too interested in the rules and not the principles. Thus I found it very difficult to apply. I am 64 now and with this I am a lot clearer thank you
The way he explains by giving context is so important, introducing the limits concept and giving the history of how we arrive at derivatives and then further showing how the 2 can be merged into a function is key to understating calculus in general.
You are not just telling me a real math, but also teach me that We can find wisdoms in everything, even in a math principle. To simply say, math is about dynamic perspective, and so life does Keep the great work sir
It was at 1:34 I realized this was never covered in my Calculus class. 😔 now I got an A in the course and never understood what I was truly trying to do. But now I know! Thanks Eddie! Forever I will be thankful to you for this.
If only I had a maths teacher like you when I was in secondary school. I learnt more in your you tube clip on calculus than I did at school. Keep up the brilliant work.
I remember my teacher just said to memorise that formula and plug in the numbers. I never did that. Depending on the question, i always try use logic to solve the question and my understanding, not memorisation. I still am on of the worst people to do maths but i wont stop trying to improve myself. ANYONE can be good at maths.
Idk if u understand the concept by now and the explanation behind the formulae learning some basic one might help in saving time for more complex problem which may lead to work out your mind more
2:14 agree. In my calculus I just shifted numbers from a to b not having considered its origin. These videos have made me question everything, or what ever remains.
I have just started Multivariable calculus after a sabbatical and needed a refresh on Calculus concepts and just chanced upon this video. Not only are the explanations crystal clear, the way he explains it (and the context) makes it so I am actually putting things together which I had never noticed before since I was literally just applying rules.
dy/dx, I studied it over 20 years ago and only now do I see where it came from!! Math is more interesting when you can see it in the bigger picture. Thanks for the education!!
Grateful that you post these online! These videos are helping me understand the fundementals in easier slower pace way. As I am taking a quick pace summer online Calculus course T_T, I feel like it's a mental sprint and I'm not good at sprinting, but I have to be. Thank you again!
Note to David Taylor (below) and Eddie. 67 y/o and trying to help my son with A level pure maths. Both of us approaching desperation and then came across this video. A big like and many thanks. Some simple concepts make mathematics so much more enjoyable and achievable: Mathematics: geometry - shapes, algebra - relationships, probability - chance, calculus - change.
I've always missed an introductory overview to any subject as this. Problem with maths is that you are normally given recipes (algorithms of some sort) when this is nothing to do with maths. I remember studying sets and rings after high school just to realise that maths are not kitchen recipes at all but something totally different. Great tutorial thank you.
Same here, even in college I'm having problems with absolutely no explanations and just expressions and formulas being thrown at me haha. Eddie's videos do truly help.
Very well explained Professor Eddie Woo. I wish I had a teacher like you in my college in India in the years late 1960s when I first learnt calculus. I am of the same age as David Taylor whose post I saw below. I had to struggle to grasp the subject. Of course now things are totally different, as India has made tremendous progress in science and technology, and in pedagogy too.
Hello ,now 2020 in India introduction to calculus for me and in 2021 again a revision to the idea of calculus..... And me being a jee aspirant.... I got my intro to the idea of calculus from both teachers (coaching+school) in a way pretty similar to Mr. Eddy woo (but he has diff. Energy ofc)... And I think I got lucky after seeing the comments maybe lucky ones ain't watch this vid and are learning something newer
A brilliant explanation of basic calculus. If only my head of maths teacher had taught it that way. This why his Express maths group flunked the additional maths exam 40 years ago on their first attempt. It's not what you teach but how you teach it. Will be subscribing for more as it's never too late to learn.
Hello sir , I'm from INDIA 🇮🇳& I teach mathematics in my rural area.I never found this concept such a way .the way of your teaching really make me feel the mathematics that I always wanted to involve in my teaching skill.finally I got som e topics of mathematics from videos but caption in English makes me less understand.I wish these videos were in Hindi. God always bless you sir & teachers like u bless us by such a teaching 🙏 THANKS A LOT SIR 🙂
The Introduction of the digital calculator in the 70 s and then Computers - ruined definitely the mind forever! Even the Manager of a German Super market saw no problem, charging me 119 Euro for 10 Eggs...recently a customer was billed 4,6 Million Euro for her groceries...Money is no problem anymore, we have infinite Credit - and debility...I bought 2 Slide Rulers from the 60s - what a relief! Switch the old rusty Brain on - what a pain...
This is a very good explanation. He could've added that f' is the Lagrange Notation, dy/dx is the Leibniz Notation and that Newton used dots to indicate derivatives.
Lol - but it’s MATH, it can’t be procrastination! There is a lot worse one can procrastinate with. (BTW - I’m procrastinating by watching because I have to fix my computer and don’t really want to.)
I never got to Calculus in 8th grade almost. More rules in geometry is why on a fisher screen projector😂. He’s giving a lot of detailed explanations to what’s going on. Quickly. Thank you! Eddie
Hi,Eddie, @ 8:46 but how did you take it out of the equation without it being h/h = 1...but it shouldn't it be stated that provided h is not 0,meaning we simply can't know what the derivative is at the point?... But then if we consider instantaneous velocity, we know its not undefined ,hmm...confusing, is calculus just about probability and approximation?
I read that Newton actually didn't invent the concept of limits. Instead, he used infinitesimals in a sort of a mathematical "hack" that upset the mathematicians of the time because it involved this idea that a really really really small "infinitesimal" number times itself = 0.
As someone who started watching your videos 6 years ago when I started uni, as a now qualified Engineer of 2 years, I am glad to see that these videos still are this damn good. You take the time to actually communicate your subject, and your passion for mathematics and teaching is clear. Just a long term viewer and fan dropping in to say "great job"! Keep it up, mate!
when you substitute f(x)= x^2. Shouldnt it be (x^2 + h) - f(x^2)/h. Because if you foil (x+h)^2, you get x^2 + 2xh + h^2. Please explain with low math words, im only a 10th grader thanks
Gradient aka slope will be delta y/delta x. So it will be (h+x)²-x²/(h+x-x). Solve it; we get =(h²+x²+2hx)-x²/h {x² will get cancelled.) =h²+2hx/h. {take h common from numerator and denominator) =h(h+2x)/h. {h will get cancelled} =h+2x Now the Lim h➡0 So we will put h=0 (p.s we didn't keep the value of h as 0 earlier in denominator because that would become meaning less and would be of no use, in Eddie's word, it would explode.) So now when we put h=0, we get 2x=2x. That is our answer. So now, the slope will be 2x, I.e, for every x, f(x)=2x. Why? When u put those values to find out the slope, x will get cancelled out and 2 as our answer which was our original answer before. Hope this helps!
If h is not zero in the beginning how is it zero at the end of the solution. What you were supposed to say is that as h tends to zero this function f(x)=x^2 gets closer to the gradient function 2x.
Man, Calculus in university would have been hella easier if the profs action mentioned all this, until this day, 20 years later, I never could figure out how the derivative rules were formed, it's so simple now. Granted, the prof that taught us ended up having 60% of the class fail...
Is the secant that we imagine necessarily parallel to the tangent? I think that, if the secant is parallel to the tangent (at any x) then the two points where the secant cuts the curve will not be f(x) and f(x+h) but two other points, one of which is a little earlier than f(x) and the second one which is a little later than f(x) on the curve of the function.
You are thinking about f(x) as a specific fixed point but it is not. It can be whatever it needs to be based on the value of x. and x+h will be a little bit further from where your initial position of x is.
In the general case: no But when the length of the chord gets smaller and smaller the secant approches the slope of the tangent. It was just in his sepcial case of looking at a circle, that the secant was parallel to the tangent and actually I am not happy with that example exactly for the reason you showed up: it confuses more then it is good for. He should have used just 2 points on the original function and demonstrate that the slope of this "secant" approaches the slope of the tangent as the second point gets closer and closer to the first one. please do your self a favour and forget the secant. It was just used as some sort of motivation of how to come up with a way to get at the tangent at one specific point. Actually calculating a derivative is much more then this.
His teaching is amazing. However, what's really amazing is the fact that he can answer a person's question so well. It's actually quite easy(for me), to give good presentations/teachings, but what actually makes it difficult, is when they ask questions! It'll take me time to understand and think of the best way to actually solve the person's question, without confusing them even further. However, Mr.Woo barely hesitated before he understood, and solved the problem. Great respect for that.
What really got me into math was one day in my first Calculus class, my teacher who reminds me am lot of Eddie, let me go on for about 5 minutes working things out in my head as to WHY the derivative is what it is and not just "what is it" and he let me figure out it's real world application and meaning myself, and all of the sudden everything we had been learning about was REAL, not just something I was being told. And then my teacher said "I can't believe you just backward logic'd yourself into finding out what a derivative is. Well done." And everything was just so joyous.
Mayuresh Bapat he found out the meaning of life
Thanks Eddie. I am a 68 yo and just refreshing my maths, with your help (because I can). When I was at school, in the 60's, my maths understanding was greatly elevated by understand the application ( to the real world) of the math being taught at the time. One application was logarithms. It was to explain the phenomena of the world around us, in one case about sound, and to calculate the compression of air when sound travels, is a log expression. It is likely that at each step, in your explanation, you would suggest where this math method would apply in the real world. The application of math, has given me great benefit, as I was fully engaged, and could see the meaning of math, and to see it being important for my future.
your 69 now. nice
@@JJJr14 Your spelling ability is crap now.
💜🤍💜best of luck💜🤍💜
That's a wonderful take on Math. I'm majoring in Mathematics and sometimes struggle to see the significance of the contents I'm taught because they seem too abstract.
Anyway, I hooe you're doing well.
Hi sir,
I am Aditya soni from India
I am impressed by your courage and love for maths, and I want a little bit help from you.
I am studying maths but I don't know how can we apply it in the real world. if you will suggest something for the resources from where i can learn the application of maths, it will help me a lot,,
Hoping for a positive response from you.
they (teachers) always told me its too complicated to explain dx/dy or we dont have the time for it :/ . this makes them look very bad now!
have you covered calculus ? or did u want to find it out early. as this litterally was what i did on my firsy lesson of differentiation
they are bad
to be fair, it is hard. he's an exceptionally good teacher.
@@nicoles_handle it's not hard at all. This is a very common practice in Australian schools where he is at.
Year 11 curriculum is the introduction with first principles and an explanation of how to get it
Year 12 you should know how calculus works well enough to be able to simply apply rules.
Trigonometric calculus as well as logarithmic calculus is not taught until Year 12 when the students should have a good knowledge of how and why calculus is what it is.
@@swordiexd i was more talking about how hard it is to convey something so abstract, and how he makes it look easy. i get foundation, but his teaching is approachable.
If I had had you as my math teacher in high school or college many years ago everything would have been so much easier. Why did I never get the explanation of why the derivative is what it is, but instead only got the final result to be accepted as gospel? These series of videos is just great, as the rest of yours that I have watched. Thanks a lot for doing this!!
When I learnt this at my high school, the teacher was too interested in the rules and not the principles. Thus I found it very difficult to apply. I am 64 now and with this I am a lot clearer thank you
The way he explains by giving context is so important, introducing the limits concept and giving the history of how we arrive at derivatives and then further showing how the 2 can be merged into a function is key to understating calculus in general.
I'm so happy I found this.
.. said a Blonde, facepalm.
Hear hear
Something about your teaching style/personality just makes me want to keep watching. Thanks
scaring the hoes pfp hell yeah
Eddie: you're a genius at clearly explaining difficult concepts - the best!
You are not just telling me a real math, but also teach me that
We can find wisdoms in everything, even in a math principle. To simply say, math is about dynamic perspective, and so life does
Keep the great work sir
It was at 1:34 I realized this was never covered in my Calculus class. 😔 now I got an A in the course and never understood what I was truly trying to do. But now I know! Thanks Eddie! Forever I will be thankful to you for this.
Enjoy how you are so patient with students and understand their perception.
You rock, I wish I had teachers like you
If only I had a maths teacher like you when I was in secondary school. I learnt more in your you tube clip on calculus than I did at school. Keep up the brilliant work.
I agree
I remember my teacher just said to memorise that formula and plug in the numbers. I never did that. Depending on the question, i always try use logic to solve the question and my understanding, not memorisation. I still am on of the worst people to do maths but i wont stop trying to improve myself. ANYONE can be good at maths.
Idk if u understand the concept by now and the explanation behind the formulae learning some basic one might help in saving time for more complex problem which may lead to work out your mind more
Just couldn't resist commenting on this one. You made maths a beautiful subject. THANKS ALOT : )
i was unlucky i hadn't teacher like you .... i am literately copying you to explain maths to my students man you are amazing Thank you.
NH I'll I'll kfkf
As a teacher myself, I appreciate your work. I'm getting some inspirations from you on improving my channel for my students as well. Thank you Sir.
You simply are a great teacher by nature I believe. Just your energy & presence are conducive to learning. Thank you massively.
2:14 agree. In my calculus I just shifted numbers from a to b not having considered its origin. These videos have made me question everything, or what ever remains.
"I want the tangent, not the secant" ... I'll put that in my bio now
bet
Thats's...actually deep man, you want the point where things converge
Lol
@@rafaels.2350 Yah, but divergent thinking is more valued in today's society. Man needs to know how to think. Think deeply.
@@particleonazock2246 But I didn't understand
Can you explain it to me
Incredibly passionate and intoxicating teacher. You rock Mr Woo.
These first three videos of his are the best explanation of calculus ive ever had…..ever….since 1997.
I have just started Multivariable calculus after a sabbatical and needed a refresh on Calculus concepts and just chanced upon this video. Not only are the explanations crystal clear, the way he explains it (and the context) makes it so I am actually putting things together which I had never noticed before since I was literally just applying rules.
dy/dx, I studied it over 20 years ago and only now do I see where it came from!! Math is more interesting when you can see it in the bigger picture. Thanks for the education!!
The way eddie explains the difficult concept is mesmerizing
A superbly gifted teacher. Thank you
Grateful that you post these online! These videos are helping me understand the fundementals in easier slower pace way. As I am taking a quick pace summer online Calculus course T_T, I feel like it's a mental sprint and I'm not good at sprinting, but I have to be.
Thank you again!
Note to David Taylor (below) and Eddie. 67 y/o and trying to help my son with A level pure maths. Both of us approaching desperation and then came across this video. A big like and many thanks. Some simple concepts make mathematics so much more enjoyable and achievable: Mathematics: geometry - shapes, algebra - relationships, probability - chance, calculus - change.
I've always missed an introductory overview to any subject as this. Problem with maths is that you are normally given recipes (algorithms of some sort) when this is nothing to do with maths. I remember studying sets and rings after high school just to realise that maths are not kitchen recipes at all but something totally different. Great tutorial thank you.
Same here, even in college I'm having problems with absolutely no explanations and just expressions and formulas being thrown at me haha. Eddie's videos do truly help.
@@toastedsniper9248 Same
Very well explained Professor Eddie Woo. I wish I had a teacher like you in my college in India in the years late 1960s when I first learnt calculus. I am of the same age as David Taylor whose post I saw below. I had to struggle to grasp the subject. Of course now things are totally different, as India has made tremendous progress in science and technology, and in pedagogy too.
Hello ,now 2020 in India introduction to calculus for me and in 2021 again a revision to the idea of calculus..... And me being a jee aspirant.... I got my intro to the idea of calculus from both teachers (coaching+school) in a way pretty similar to Mr. Eddy woo (but he has diff. Energy ofc)... And I think I got lucky after seeing the comments maybe lucky ones ain't watch this vid and are learning something newer
A brilliant explanation of basic calculus. If only my head of maths teacher had taught it that way. This why his Express maths group flunked the additional maths exam 40 years ago on their first attempt. It's not what you teach but how you teach it. Will be subscribing for more as it's never too late to learn.
Hello sir , I'm from INDIA 🇮🇳& I teach mathematics in my rural area.I never found this concept such a way .the way of your teaching really make me feel the mathematics that I always wanted to involve in my teaching skill.finally I got som
e topics of mathematics from videos but caption in English makes me less understand.I wish these videos were in Hindi.
God always bless you sir & teachers like u bless us by such a teaching 🙏
THANKS A LOT SIR 🙂
his face at 6:40 lol he's so excited about math
I thought i was the only one to be honest!!!!
The Introduction of the digital calculator in the 70 s and then Computers - ruined definitely the mind forever! Even the Manager of a German Super market saw no problem, charging me 119 Euro for 10 Eggs...recently a customer was billed 4,6 Million Euro for her groceries...Money is no problem anymore, we have infinite Credit - and debility...I bought 2 Slide Rulers from the 60s - what a relief! Switch the old rusty Brain on - what a pain...
This is a very good explanation. He could've added that f' is the Lagrange Notation, dy/dx is the Leibniz Notation and that Newton used dots to indicate derivatives.
I really like this lesson. Its just great. Wish i had the history about all maths topics i learnt at the elementary stage.
this teacher deserves my subscription
Watching calculus lectures to avoid comp-sci HW is a level of procrastination I've not reached before 😅
Lol - but it’s MATH, it can’t be procrastination! There is a lot worse one can procrastinate with. (BTW - I’m procrastinating by watching because I have to fix my computer and don’t really want to.)
I never got to Calculus in 8th grade almost. More rules in geometry is why on a fisher screen projector😂. He’s giving a lot of detailed explanations to what’s going on. Quickly. Thank you! Eddie
Wow, his students are also good that they could raise questions because of how knowledgeable they are that is also because of Eddie woo
Hi,Eddie, @ 8:46 but how did you take it out of the equation without it being h/h = 1...but it shouldn't it be stated that provided h is not 0,meaning we simply can't know what the derivative is at the point?... But then if we consider instantaneous velocity, we know its not undefined ,hmm...confusing, is calculus just about probability and approximation?
Eddie woo is the best explainer of mathematics on the youtube.
for a guy who never understood maths, this guy made me love maths.
I just sat through a 1h50m lecture on college calculus and learned just as much from woo on youtube in 40 minutes
5:05 "...you divide by zero, it explodes." for some reason that made me chuckle
Excellent Teacher!! Well done 👍
Wish I had of known the whole idea of these ideas before. Thanks 🙏
your videos are awesome and you go into so much more detail than my prof or maybe you just explain it in a better way. Thank you.
U are amazing finally understanding what calculus means rather than memorizing a bunch of rules
God bless u
I read that Newton actually didn't invent the concept of limits. Instead, he used infinitesimals in a sort of a mathematical "hack" that upset the mathematicians of the time because it involved this idea that a really really really small "infinitesimal" number times itself = 0.
Historically, Newton was not being well liked at his time. Sad sad genius..
As someone who started watching your videos 6 years ago when I started uni, as a now qualified Engineer of 2 years, I am glad to see that these videos still are this damn good.
You take the time to actually communicate your subject, and your passion for mathematics and teaching is clear.
Just a long term viewer and fan dropping in to say "great job"! Keep it up, mate!
I noticed a great and very good math teacher today ... 2020
"...because if you divide by zero it explodes..." you said it so cool, and casual lmao; that was awesome!!
Excellent explanation and method/pace of explanation.
I wish I have watched this 9 years ago before dropping out of engineering school. 😅😂😂😂
when you substitute f(x)= x^2. Shouldnt it be (x^2 + h) - f(x^2)/h. Because if you foil (x+h)^2, you get x^2 + 2xh + h^2. Please explain with low math words, im only a 10th grader thanks
Gradient aka slope will be delta y/delta x. So it will be (h+x)²-x²/(h+x-x).
Solve it; we get
=(h²+x²+2hx)-x²/h {x² will get cancelled.)
=h²+2hx/h. {take h common from numerator and denominator)
=h(h+2x)/h. {h will get cancelled}
=h+2x
Now the Lim h➡0
So we will put h=0 (p.s we didn't keep the value of h as 0 earlier in denominator because that would become meaning less and would be of no use, in Eddie's word, it would explode.)
So now when we put h=0, we get 2x=2x.
That is our answer. So now, the slope will be 2x, I.e, for every x, f(x)=2x.
Why? When u put those values to find out the slope, x will get cancelled out and 2 as our answer which was our original answer before.
Hope this helps!
2:42 that's the cleanest dotted line circle i've ever seen
The guy who raised the 0/0 question is going places
I just want to ask.. Mr. Eddie.. From where do u get those stuffs.. How do u get so clear picture of everything
You don't need to know it might be his secret....😮
Me, 5th year Engineering student. I passed the advanced Engineering math in 4th year, Now watching this!!!
That jumper looks really comfy
shaandaar jabardast zindabaad
RESPECT FROM INDIA🌱
maybe i shouldnt have named myself agent delta... it gets weird people using your name in casual maths
Agent Delta, your name makes a difference.
🤣🤣
Best maths teacher ever
What an EXELLENT professor.
Very good explanation am interested on but can you put more vedios on this in difficult situation
I am 13 and this video helped me a lot!
wished i saw this when i was doing my A levels back in 2013
Love this guy great teacher!
If h is not zero in the beginning how is it zero at the end of the solution. What you were supposed to say is that as h tends to zero this function f(x)=x^2 gets closer to the gradient function 2x.
Great teacher amazing
In the usa we call year 11, 11th Grade in high school and 12th grade (seniors) is the last grade in high school before college (university)
You have answered the question of the pharos.
Wish I had same type of explanation in my college days....Calculus I now guess is to do with non linear behavior of objects and phenomenon around us.
Thank you so much sir.. your teaching is just like magic 💓
I wish I had a teacher like you during my 11th class. But it's too late💔
We need to see the former students of this great professor. I am certain they're thriving in a mathematical careers.
Calculus was my Archils’s Heel in Engineering School. Yes, we were given were rules to follow. But, I never realized The Concept.
I hate math, but I am watching this guy while drunk and learning what I hate most calc. I am already done with college, but ya this is big brain time.
I am so freaking happy I found your channel! Thank you!
I wish I knew about you before I wrote my advanced level exams 🥲
Man, Calculus in university would have been hella easier if the profs action mentioned all this, until this day, 20 years later, I never could figure out how the derivative rules were formed, it's so simple now. Granted, the prof that taught us ended up having 60% of the class fail...
Sir i m in love with ur maths concepts and the way u approchd....grt siir love u
I’m a 11 year old watching college math that looks like calculus 2 and pop up in my recommended
Dude you're amazing at explaining haha thank you very much :)
f(x) = f(x+h)-f(x)/x-h unlike f(x) = f(x+h)-f(x)/h would the 2nd function make sense.
This is incredible, I love it!
Holy bat signal, Batman! Eddie illuminated all that notation goop for me. I feel like Neo - " I know kung-fu!"
how did we derive at 2^2+2hx+h^2-x^2
HOW do you teach with so much noise?????
Your the man . Appreciate it 💪🏾
How did he get x^2 + 2hx+h^2-x^ from (x+h)^2-X^2??? Is that correct???
his students are the luckiest maths students on the planet
Amazing. I teach math and this is fantastic!!
I’m in university and the only problem is that my calculus teacher is not you.
He explains like the goal is to confuse as many kids as possible.
Is there a Function for a spiral?
Yes. In polar coordinates, the function r=theta, gives you a spiral.
Tjanks for helping me understanding calculus i am in 9 but i love calculus thanks a lot
Is the secant that we imagine necessarily parallel to the tangent? I think that, if the secant is parallel to the tangent (at any x) then the two points where the secant cuts the curve will not be f(x) and f(x+h) but two other points, one of which is a little earlier than f(x) and the second one which is a little later than f(x) on the curve of the function.
You are thinking about f(x) as a specific fixed point but it is not. It can be whatever it needs to be based on the value of x. and x+h will be a little bit further from where your initial position of x is.
In the general case: no
But when the length of the chord gets smaller and smaller the secant approches the slope of the tangent. It was just in his sepcial case of looking at a circle, that the secant was parallel to the tangent and actually I am not happy with that example exactly for the reason you showed up: it confuses more then it is good for. He should have used just 2 points on the original function and demonstrate that the slope of this "secant" approaches the slope of the tangent as the second point gets closer and closer to the first one.
please do your self a favour and forget the secant. It was just used as some sort of motivation of how to come up with a way to get at the tangent at one specific point. Actually calculating a derivative is much more then this.