Continuity of a Function | Two Variable Function | Multivariable Calculus

[@gajendrapurohit]

Thanks for your comment, your appreciation always motivate us to do such kind work. Join Telegram Channel : t.me/mathsbygpsir Instagram Handle : instagram.com/dr.gajendrapurohit/ Facebook Page : facebook.com/Dr-Gajendra-Purohit-453775988491992/ Unacademy : unacademy.com/@Dr-GajendraPurohit Link to B.Sc. Maths Playlist : bit.ly/34tTTdc Link to Engineering Maths Playlist : bit.ly/2OQ7Uvd Link to IIT-JAM Maths Playlist : bit.ly/2sh9pei Link to GATE (Engg.) Maths Playlist : bit.ly/35EAPct Link to IAS Optional Maths Playlist : bit.ly/2rwkOqj Link to CSIR NET Maths Playlist : bit.ly/2R8sUjV Link to Aptitude Playlist : bit.ly/3ewDR7z Link to Mathematical Physics Playlist : bit.ly/2NvRHLJ Link to Abstract Algebra Playlist : bit.ly/2A70LUb Link to General Aptitude For CSIR NET : bit.ly/2ZeWpma Follwing Topics are also Available 1. Differential Calculus : bit.ly/2OTYXB0 2. Integral Calculus : bit.ly/34rLA1R 3. Differential Equation : bit.ly/37IOlO1 4. Partial Differential Equation : bit.ly/2OM5iyA 5. Complex Analysis : bit.ly/2OP8hGp 6. Numerical Analysis : bit.ly/2QYVQuy 7. Integral Transform (Laplace, Fourier & Z-Transform) : bit.ly/37HRKg9 8. Statistics & Probability : bit.ly/2DmOt7Z 9. Operation Research : bit.ly/2pYYRjp 10. Matrices (Linear Algebra) : bit.ly/2OOBSzO 11. Fourier Series : bit.ly/34u7iC9 12. Vector Calculus : bit.ly/2qICwXO 13. Theory Of Equation : bit.ly/2XU9y33 14. Special Function & Series Solution : bit.ly/2XRSU4l 15. Infinite Series : bit.ly/37K6gUI 16. Group Theory : bit.ly/3ieUze2 Please share it with your Friends Thanks Dr.Gajendra Purohit

[@humairasiddiqui9120]

Sir aapke videos bahut helpful rhte h hmlogo ke liye...Thank you sir

[@Simran-jk6yo]

Sir could you plz tell does your videos contain b. Sc maths hons. Whole Syllabus of delhi university

[@realtimestudy3410]

Sir aap bsc 2nd year ke liye limit and continuity Pura syllabus cover Karke Ak video post Karna please🙏🙏

[@missmamta8398]

It is very helpful video Sir for all mathematician students...... Your teaching way is very good and voice is also very clear.... I belong from UP (Ayodhya)... 😊😊

[@elonmusk1953]

It is very helpful for us.thank you so much sir love from PAKISTAN

[@vishwajeetkumar1360]

Bhai... tum galat jagah pe apna time invest kr rhe ho... move in right direction as your government and terrorist organization wants.

[@deepanshurawat4241]

@@vishwajeetkumar1360 ekdam bewakoof ho kya

[@vishwajeetkumar1360]

@@deepanshurawat4241 bsdwale chachaa... gyani na bano jyada

[@SAURABHSINGH-gt8zw]

@@vishwajeetkumar1360 waah bhai...kya baat bole ho...dil jeet liya

[@player-ne6hs]

Pakistani elun 😅🤣

[@smartattributeslearning1559]

Extra ordinary teaching ability Thank you sir

[@Islam99451]

University ma lakhon fees dy kr KZbin pr parh kr kis kis ko maza aaraha😢😢😢😂???

[@ripamhazarika2360]

Sir last question me jaha continuous proof krna hota hai, waha pe aap ne "limit exist hai" ye proof karne k liye sirf y=mx leke dikhaya hai... Aur baaki jo bhi path lu limit same hi aayega ye bataya hai... Par sir hum ye generally kaise proof kare ki limit exits kar raha hai? Kyu ki there exist infinite paths.. har ek path ko leke kaise proof kar sakte hai... Ho sakta hai kisi path se limit same naa aa raha ho... Please explain

[@NisargJain]

In general, hume neighborhood check krna hota hai. For last example, hum x=rcost and y=rsint le skte hai with r tending to 0. This will cover complete neighborhood of (0,0). Usko put krne pe function ki limit 0 jaa rhi hai hence limit exists.

[@tarunyadav9664]

But nisrag,by taking x=rcost and y=rsint,we are only covering circular paths along (0,0),there are infinitly many other paths,so to proof this we have to use epsilon delta defination

[@gauravsinghvyas4492]

Aap bahut achha padate ho sir very very thank you sir itni jyada helpful video banane ke liye

[@prashasthidiangelo6865]

In the last question, to show it is continuous everywhere, we need to consider all the paths right, but you only considered y=mx, and x=y, I am little confused. What about approaching from a different path like a curve.

[@player-ne6hs]

It is possible buy the (x,y) should be( 0,0 ) and according to it u have tonselect a curve

[@Ashish-gb7fy]

Check whether limit exists along a particular curve, and find the limit value. Then confirm limit exists using epsilon-delta definition

[@Aspirantsrajit1053]

Thank sir aap ke video mere liye bahut helpful hai

[@harimohansaini8917]

This video is very helpful for me

[@FULLBass-nz1he]

00:01 The topic discussed is limit continuity and differentiability for the function of two variables. 01:15 Continuity of a function of two variables is determined by the existence of a limit and its equality to the value of the function. 02:21 Continuity of a function requires that the limit exists and the function value equals the limit. 03:53 The function is not continuous because the limit is not equal to the value of the function. 05:52 Example of a two variable function 08:01 Example of continuity of a function 10:08 The function has a limit of 0 even when m equals 1. 12:08 Next video will discuss differentiability and function of two variables Crafted by Merlin AI.

[@siddharthsahu1474]

You videos have really helped me regain my focus in the subject!! Thanks a lot!!

[@hajimeanime]

Agar ×-y rahe to? ×=-y assume kare?

[@nehayadav1013]

Sir aap itna achha pdhate hai ki coment likhkr bhi nhi bta skte....... Thanku so much sir

[@vijaytandi5406]

Thanks sir please make more video on bsc mathematics

[@Randomnoob690]

very good teacher , really help me to pass my semester exams

[@Randomnoob690]

good comment

[@vinodjangid8858]

Show these definitions by drawing graphs.

[@mohitjariwala8011]

Bahut aacha lagta he aapka content

[@elizandramanuel4438]

Thanks teacher, you really help me to understand this topic.

[@ahmedjaan5132]

Sir in previous question we have checked at path y=Mx only.but in 2nd one we use another path where valu is not zero..so tell me sir can we judge it behaviour by only single path or we have to change path,is there any shortcut

[@R_i_c_h_a]

Same questionera bhi h

[@pranshusaini8791]

my exam is after 3 days I hope ki mene apki video pehle dekhi hoti

[@brandshanisinghrajpoot5330]

Bhut sundar guru deo

[@rudranarayan3725]

Best explanation I ever seen

[@bikrambhai---yt.9016]

very helpful video for me❤

[@aafiyasheikh82]

Thankyou sir for this explanation

[@kesariclasses]

Thanks for your trick

[@arnabsadhu6154]

Thank you sir... Very much helpful content... Really helps me with my college studies... I m B tech from NIT Durgapur 1st year

[@Nazimkhan771]

Love you sir from mumbai University

[@meenakshisharma7025]

Thanku so much sir for helping us alot 👍👍

[@sittalthapa3296]

Thank you sir from nepal

[@SurajKumar-yy2lh]

THANKS SIR MY ALL DOUBTS ARE CLEAR IN LIMIT & CONYINUITY 😇😇😇😇😇😇😇

[@aryansingh8562]

Love you sir ❤👏

[@Neha-mv1xx]

Sir plz.. Sequential nd uniform continuity ... Par bhi video bnaa dijyee plzzz..

[@Agrarian06]

Sir Question at 2:50 was same question in BPSC 65th mains math optional paper

[@lakshyagupta2426]

♥️

[@hemendrasinghtanwar592]

Sir please upload lecture on real analysis

[@triangleeducation17]

Sir thanks a lot aaj mera btech 2nd year ka exam tha...4 din se only aapke lecture dekh rha tha...and I scored 80/100...again thanks a lot sir..

[@Neha-ep6cv]

🧐🧐 80/100 ..... 😒 Mujhe kyu nhi aata itna jyada.....

[@player-ne6hs]

Wao

[@jayjoy]

Kya aakhir me padhna start kiya tha?

[@gyanjyotikashyap4766]

Best content of india

[@Upscwalla_26]

Thanks guru ji🥰 Mahadev bless you 😊🙏🙏

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Thanks alot sir☺️☺️☺️☺️

[@ShashankSingh-jl2wy]

Sir you are best

[@Gauravsharma-1209]

Thank you sir for uploading such great videos

[@Ankit-yv4tj]

Sensitivity analysis ka Vidio banana ji

[@Har-Har-mahadev-]

Thank you so much sir today my all dout of this topic is clear

[@AbdulKareem-sx2pu]

Mashallah thanks for it❣️

[@aadhyadas9588]

Sir please start lecture on fluid dynamics. I am preparing for upsc math optional

[@everyshadeofgreenunderthes6580]

Hi I'm preparing for state commission

[@twop6505]

Sir IIT jam ke syllabus ko shuru se video bana kr playlist me daliye 🙏🙏sir

[@Suraj-ur6dz]

thanks sir , your videos are so helpful

[@ridipkalita430]

Thank u sir...you are really great

[@chaliyaashok9922]

Very very nice sir ji

[@gsamrutiya7326]

at: 10:25. My question is there are only y=mx path to check our limit. What about those curves whose passing through (0,0)

[@player-ne6hs]

Yeah u can

[@saurabhgupta2301]

nice lecture

[@tushararya7005]

good content, keep it up, it is possible to be family of IIT MADRAS

[@Rameshmeher891]

Love from America ❤

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@@Rameshmeher891 America mei kaha rehte ho bhai ??

[@sushanty993]

Thanks 🙏

[@sakshiaggarwal4492]

Superb going on sir......great done sir

[@maniupadhyay8684]

Kya hi kehne sir ke

[@arunoberoi3647]

Never give up... ✍️👨🏻‍💻👨🏻‍💻🖊

[@craftishme1142]

Thank you so much sir ...this lecture was very helpful to me...

[@backtobasics789]

Very helpful vedio sir

[@Harshjain11111]

8:20 pr apne bola ki ek trick use me lenge jiske ander x²=y⁶ kiya, sir esa kis condition pr use krte h

[@rupeshnarnavre8546]

Sir, changing polar co- ordinate ho sakta he ?

[@yashpal1523]

Very helpful for us

[@takumtame4612]

Sir. Discuss continuity of f(x,y) = 0 ( when xy not equals 0) and 1 ( when xy equals 0)

[@ambeshkumar3547]

Sir plz ek pdf bhi attached kr diya kro questions ki discription me taaki thoda help mil jaaye otherwise thank you sir and sir plz mechanics ki vdo daaliye sir for bsc 2nd year

[@TechMarcell]

👍👍👍👍👍👍😀😀Liked the video next video

[@mdibrahimkholil6856]

Sometime we take y=mx and sometimes not and sometime x=rsin @ Y=rcos@ When what type of methods we use. Sir ans plz.

[@mdibrahimkholil6856]

And somewhere uses inequalities

[@PremKumar-mu9bf]

Amazing mathod sir

[@deepakmishravlogs3327]

Sir geometry pr bhi video banaye

[@lutfunnahar5271]

You really explained it so good.

[@VivekYadav-hb9ej]

Excellent sir

[@rickypatel7421]

Sir your voice is so pompous 😊

[@virendrayadav432]

You are great sir

[@memebaaz4005]

Sir 4.32..why we take y=mx,?

[@upscwithmeghwal1642]

Bcz in question asked check continue at origin (0,0)and path y=mx is also pass through origin

[@Myworld-fv8bj]

Awesome sir respect

[@matiullah9044]

Grt sir g love u

[@ankurdubey8424]

Verry helpful

[@twop6505]

Sir IIT jam mathematics preparation ke liye koun sa book achha hai

[@RockStar-fv5sn]

Thanks sir, very useful

[@abhishekpandey1829]

Awesome lecture sir

[@prakashupadhyay9445]

In the last question, If a limit exists for the y=mx curve, then it does not say that limit exists at that point. It may be possible that the limit doesn't exist at some path.

[@jigardevjani9245]

Yaar samajh nahi aaya ki kehna kya chahte ho ?

[@chendukishore5417]

Please do videos on real analysis also sir please

[@VIPINuph9234]

Genuinely i m thankful to u bcoz ur all the lectures helps me alot during exam as ur videos are very short having all the imp. Concepts

[@sunilbishnoi3496]

A lot of thanks sir

[@omparmar1915]

very nice sir ....OP

[@palashghosh8208]

Sir at the last example what is the garanty that along any other path it will give the same value?

[@kakulibishal8971]

Thanku sir🤩

[@ayazfarooqui2193]

Sir why does we have taken y = mx

[@rkvcherry5535]

Not only y=mx we can also take y=mx^2, y=mx^3 etc...

[@GreenArrow17]

Sir, Please upload some lectures that cover the syllabus of JAM Mathematical Statistics paper also. Thank you!

[@arlodhi9826]

Very nice sir

[@4hostelboys]

Awesome sir

[@ankitbhardwaj4784]

Nice video

[@geeta5011]

Sir Can I watch your video for bscg.

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Good containt

[@papaypurhariyawan5287]

Sir algebra mai subgroup ke baad aur vedio bana digye sir plz 13 se exam hai plz

[@BS---qd7qd]

Thank you so much, sir

[@15-shabirahmad99]

Love from Kashmir

[@soubhagyaranjanprusty6953]

Thanks a lot sir. ...

[@smritisneha2789]

Sir in example 2nd can we say that the function is continuous everywhere except (0,0)??? Please reply sir.....

[@gitanshugupta8556]

Awesome work sir !!!

[@sejalbhatt2611]

Hello sir.. Aapne ye jo continuity samjayi h ye konsa method h means is method ka kya naam he...????