Thank you for your beautiful explanation. It helped me a lot in understanding mathematical problems. I did not understand anything from the book after your explanation. I understood, thank you very much 👏🏻👏🏻
Right answer for Q4, step 1: g(1,2) = 0, step 2: lim of (x^2 + 4y) as x,y approaches 1,2 = 9, step 3, since value for step 1 is not equal to that of step 2, the function is not continues at (1,2).
Your video is really helpful can't thank you enough, the explanation s very clear too u are a great teacher trust me keep it up❤ live long mister but if you have worked examples on level curves and graphs of several variables please Baay'een sitti gammade ulfaadhu!!!!!!!!! replay me soon
Thanks alot for such videos❤. Can we solve question 6 without using polar coordinates like if we take y=0 then equation will be sin(x^2)/x^2... then we apply Lhopital rule and get the same answer. 21:38
Brother, how do I know which line/curve to use to approach the equation to check if limit exists like you chose y=x in Q5? Is there any method for it or is a guess through practice?
Your videos are very helpful, but l am a bit stuck as to where l should actually use the polar coordinate approach, how do l necessarily know that it applies here.
It comes by experience, you can't really tell, but then as you solve more and more examples, you get to know where exactly to use it. Thanks so much for your words of appreciation. Where do you watch me from?
Since the limits along different paths are not the same, the limit does not exist. Because the limit does not exist uniformly, this discontinuity is not removable.
yes you can approach the limit point from different directions. In fact you can choose to use polar coordinates all the time, but it's usually dependent of the question. I feel with much experience gathered as a result of constant practice, you will know the best approach to use, because sometimes approaching from different directions will help you to get the results faster
polar coordinates were not used in Ex 2 and 3, but rather Ex 6 and 7. In addition i want to understand that you want to ask why eg 1 was quite simpler as compared to 2, and 3. Eg 1 is a polynomial function in x and y, hence it is continuous everywhere, however for eg 2 and 3, we have a rational function, a rational function is continuous everywhere except where the denominator is zero making the whole function undefined, at that point, the function is discontinuous.
This topic kept troubling me...finally from your amazing video, I learnt the process..
You have explained beautifully..
Thank you sir 🙏🏻🙏🏻🙏🏻
Happy to help
Thanks so much sir and I like your teaching style.
Great, thanks so much.
Sir I am watching from India, you are my favorite teacher.
Aww thanks so much. Good luck
Everywhere i go in my field,i find your videos😂😂 i guess??
Wow that's amazing
same here😁😁😁
Thank you for your beautiful explanation. It helped me a lot in understanding mathematical problems. I did not understand anything from the book after your explanation. I understood, thank you very much 👏🏻👏🏻
You are most welcome
This video is very helpful. Thanks to this, i was able to understand our lesson
You are most welcome
thank you so much sir, i can finally understand how to do it now
That's amazing
Can’t thank you enough. My maths professor make these seems so difficult and i was really struggling to catch up.
Awww sorry about that. But finally, you understand now. Thanks for watching and commenting to show your appreciation.
Tell me where you come from?
❤❤❤
thank u for this clear explanation
Most welcome
sir I am from India love you so much sir you are gem
Thank you very much
Your a genius! Life saver!!
awwww thanks so much
Right answer for Q4,
step 1: g(1,2) = 0,
step 2: lim of (x^2 + 4y) as x,y approaches 1,2 = 9,
step 3, since value for step 1 is not equal to that of step 2, the function is not continues at (1,2).
concept crystal clear
i don't know why in every other vidio i watched in yt every one is doing 0/0=0 which is creating big confusion
Owww
Thanks for finding me.
What's your nationality ?
Thanks man. Very helpful
Glad to hear it!
Your video is really helpful can't thank you enough, the explaination s very clear too u ar a great teacher trust me keep it up❤
Thanks so much Jobe.
No I should be d 1 thanking you may Allah bless you
I know right...
Where do you watch me from?
In Morocco, an international student from the Gambia
Your video is really helpful can't thank you enough, the explanation s very clear too u are a great teacher trust me keep it up❤ live long mister but if you have worked examples on level curves and graphs of several variables please
Baay'een sitti gammade ulfaadhu!!!!!!!!! replay me soon
Thanks so so much, will consider those too
Billions and trillions of thanks ♥️
Aww thanks so much 🥰
Where do you watch me from?
@@SkanCityAcademy_SirJohn I'm watching you form Pakistan
@mughal___hu-------yara aww that's great. Thanks so much
Very good. Thanks 🙏
Thank you very much
Tnx sir🙏🙏 your video is help full me
You are most welcome
Thank you so much.... Actually I have exam in 2 days... And I cleared one of my confusing topics...
😍that's great to here
Thank you so much sir
You are most welcome..... Good luck.
Thank ❤... From Tamilnadu (India)
Aww you are most welcome
Thank you so much
Most welcome
Thanks alot for such videos❤. Can we solve question 6 without using polar coordinates like if we take y=0 then equation will be sin(x^2)/x^2... then we apply Lhopital rule and get the same answer. 21:38
If you do not want to use polar coordinates, then you need to approach with more than one line, so let's say after y=0, you do y=x, y= -x and so on.
Best 🎉 Love ❣️ from Pakistan
Thanks so much for watching, and good luck in your studies
nice
Concepts are very clear. But please, when and how do I know I have to use the polar co-ordinate form? Is there any exceptions?
It's based on experience. When you solve over and over, at a point you will know which approach to use for various questions
Cant we use just a normal approach that we solve the question in two ways , along x-axis and along the line y=x??
Brother, how do I know which line/curve to use to approach the equation to check if limit exists like you chose y=x in Q5? Is there any method for it or is a guess through practice?
It's a guess. You just choose any simple line to solve with
@SkanCityAcademy_SirJohn thank you
Why you took only y=x...
We can also take y=mx ,y =x½,x¼,etc... And when to take these line equations
The thing is we can take any line y = mx + c, buy we want to take a simpler line equation for easy computation.
Your videos are very helpful, but l am a bit stuck as to where l should actually use the polar coordinate approach, how do l necessarily know that it applies here.
It comes by experience, you can't really tell, but then as you solve more and more examples, you get to know where exactly to use it.
Thanks so much for your words of appreciation.
Where do you watch me from?
What if I use let x²+y² = t
What if the question also stated that also find whether is function has removable discontinuity?
How will we determine this?
Since the limits along different paths are not the same, the limit does not exist.
Because the limit does not exist uniformly, this discontinuity is not removable.
When to take y= mx either anyone of y=x½,x¼,etc... while finding limit ? you just only took y=x
Sir in the last question why polar coordinates were used?can we do it by approaching x axis,y axis,y=mx?????how to know when to use polar coordinates?
yes you can approach the limit point from different directions. In fact you can choose to use polar coordinates all the time, but it's usually dependent of the question. I feel with much experience gathered as a result of constant practice, you will know the best approach to use, because sometimes approaching from different directions will help you to get the results faster
why wasn't polar coordinates used in the first and you used them in the second and third?
polar coordinates were not used in Ex 2 and 3, but rather Ex 6 and 7. In addition i want to understand that you want to ask why eg 1 was quite simpler as compared to 2, and 3. Eg 1 is a polynomial function in x and y, hence it is continuous everywhere, however for eg 2 and 3, we have a rational function, a rational function is continuous everywhere except where the denominator is zero making the whole function undefined, at that point, the function is discontinuous.
Is It okay to put it as (r,theta) approaches (0,0)
Kindly reference the time in the video for easy identification of your question
24.44 -25.30
Instead of just writing r->0 is it correct to have it as (r,theta)->(0,0)
@emeldahowell8668 yes please, you can
@@SkanCityAcademy_SirJohn Thankyou
when do we use the polar coordinates method?
You can use it anytime, just that that approach does not also confirm the limit of the function...
i don't understand why u didn't use the HR in the first example.
same idk why
if you're required not to use HR will you know how to solve it? Im an engineering major and we're not allowed to use HR in exams lol
For example 4, why did you refer to (0,0) and not (1,2)
you are perfectly right, i was supposed to reference (1,2) and not (0,0), that was a mistake from my end. Thanks so much for notifying me.
could you go through that part in another video?@@SkanCityAcademy_SirJohn
Noted