Differentiability | 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

[@SandeepSingh-kq2sx]

Sir mera is year b. sc 1st year hai main avadh university se hoon sir aap jo pdhate hain acche se samajh mein aataa hai but one problem hai agar aap differentiability of functions of one variable pe video chhod dete to aapki mahaan kripa hogi

[@suhanisahu7536]

Hello sir ... Sir x³-y³/x²+y² Cake ques ki limits y=MX nd y=x rkh kr nikalii jayein tih exist krrhi hain ....but apne vo ques doosre type se solve kiya h toh ans alg horha ...pls clear too much confused🥺

[@AnshKumar-jw3dp]

Sound of chalk while writing is so satisfying ❤️

[@mohamedjunaid598]

i thought i was the only one who liked that sound

[@darthdaenerys]

chalk asmr by gp sir

[@MuhammadBilal-us5ic]

JBH

[@IITWALALADKA]

NOW IT IS JUST A NOSTALGIA FOR ONLINE CLASSES

[@ramanjangra7465]

Hann... 😊😊🔥

[@prathikkundaragi9523]

sir, I think we can not confirm the existence of the limit just by checking in any 2 random paths. limit existence should be shown only by epsilon-delta method whereas non-existance can be shown by choosing different paths.( please correct if I am wrong)

[@tayfunyegul5413]

Yes you are right

[@AdityaSingh-qn6pi]

The Epsilon delta method gives you the most accurate result

[@amitgangwar3996]

@@AdityaSingh-qn6pi not only most accurate , that is the definition bro

[@hardikjain5060]

Yes bro you are right 💯 It seems sir said it mistakenly

[@RegisteredLate123]

exactly

[@deeplaxmisingh1242]

You are the best teacher in the world in mathematics sir

[@alokkumarkalagodi5831]

Sir at last problem Fx(0,0) and Fy(0,0) value 1? Bcz of lim h tends to 0 at sin1/h hole devided by h will be 1?

[@hari43i]

0 not 1

[@suchananag]

Yes,it will be 1 because lim(h->0){sin(1/h)/(1/h)}=1.

[@iitiantalks2538]

@@hari43i how 0 explain it

[@shreyakesarwani343]

Yes I have the same doubt

[@heyyatif6062]

@@suchananag It wont be zero as lim h->0 (sinh)/h = 1 but lim h->0 sin(1/h)/(1/h) is like sin(∞)/(∞) which is not defined so h^2sin(1/h) will be 0

[@Rakeshkumar-jf4ty]

Very nice sir thank you so much sir 🙏 🙏

[@nagigaming694]

Sir in last ques if we find fx it comes to be 1 not zero as limit (h^2 sin 1/h )/ h and limit h tends to 0(sin 1/h )/(1/h ) = 1?

[@vandanasharma-hy4mv]

we take[ lim h->0 sin(h)/h =1] not 1/h bcoz lim h->0 (1/h) = infinite

[@banidhanagar6951]

​@@vandanasharma-hy4mv I think tumhein ek baar sin ka expansion use krke Solve kr lena chahiye

[@akshattheintrovert3153]

@@vandanasharma-hy4mv Kya likh rha hai bhai. fx=1=fy hi shi hai. I think sir book se tepne ke chakkar me galat likh diye.

[@karanjaiswar9122]

In the last sum value of fx=1 & fy=1 using standard limits you took 0 sir.

[@kamlendusingh482]

Same doubt

[@RahulKumar-sc6er]

Sahi kaha bhai

[@iitiantalks2538]

Yes that is also my doubt

[@user-wh7xl5uz8e]

fx and fy is 0 only Lim h->0 hsin(1/h) =0

[@poojamishra944]

Very well explained sir... Plz upload young's theorem too.

[@rptt620]

Easy h bro wo theorems

[@soniagiaswal1843]

Your are the best sir I m watching your many videos 👌👌👌

[@satyabhamasahoo2801]

Now I am watching this and finally my doubt is clear 🥰thank you sir🙏

[@nehayadav1013]

🙏🙏🙏🙏🙏 sir aap students ke God hai

[@pawankumawat5102]

So useful video . thanks sir

[@salmanshaikh1810]

Love u sir 😘❤️❣️..... Apke sabhi videos boht hi helpful h...... Thanks a lot sir.........

[@VikasKumar-jz5mv]

Sir Great Explanation ❤️❤️🙏🙏🙏

[@Saurabhmishra462-NITJSR]

Sir you are extraordinary teacher 💗💗 the way you solve each problem is looking like a wow🎉🎉

[@payal8728]

Thanks sir, Aapki videos se bohot help ho jaati hai😊😊

[@deekshachaturvedi5372]

U r best sir🙏I know you from last 1year.....every day I get motivated from your lifestyle the way you do hardwork... And passionate for teaching us.... U r director in college... U r best educator on undacademy.... U r best on youtube.... And so much... The way you manage....give your best inspire me daily... 😊thanku so much sir😇

[@gajendrapurohit]

Thanks disksha ji

[@dalitshiv834]

Very Good Deeksha👍🏼👍🏼

[@upadhyaysunilmath9603]

Sir you are the best Aap bahut hi aasan tarike se padhate jai

[@vmgphysicsclasses1072]

Sir aap k video se bahut jyada hi help hoti hai

[@anikaitdash6519]

Dr. GP Sir - OG Teacher for Math

[@sanamsanamrani6206]

Very great method of teaching JUZAKALLHA

[@ayushagarwal69]

@17:13 when we put y=0 , how did the function become 0 , 1/y wala term will be unsolvable right? Then what to do?

[@swastiktiwari7066]

At 5:20, I think the correct proof for continuity of function at (0,0) is lim(x->0,y->0) xy/sqrt(x^2+y^2) = lim(x->0,y->0) 1/sqrt(1/x^2+1/y^2) = 0 = f(0,0). [since 1/x^2+ 1/y^2 is invariant to sign of infinitely small x and y if abs(x) and abs(y) are same]

[@Shorts-ej4so]

INDIA KA NUMBER 1 KZbinR H AAP WOH TIME DOOR NAHI......

[@Divyaprakashanditsmasti]

osm sir my all concepts cleared

[@abhinaygautam2910]

Thank you sir for explaining this in very short time🙏🙏👏👏

[@ravibadwar2002]

Thnku so much sir🙏🙏🙏

[@studywithrahul7215]

Thanks sir very helpful video

[@harsinghmandavi]

Thank you sir you explain very nicely in short time

[@shrawankumarpatel2148]

Thank you sir so helpful for msc pre

[@sunidhi206yadav]

Very very helpful video 👍

[@naveenchandpandey1486]

Dhanyvad sar aap ki video bahut acche rahe

[@shaliniyadav4822]

Nice explanation ✌

[@vaishalipatley3318]

Thank you so much sir aapke en videos se Bhut help milti h

[@Prince-cm8jx]

Great lecture❤️❤️

[@hari43i]

No any sir like you ❤️

[@hari43i]

Really great sir ❤️🙏

[@blueberry23]

Thanks sir, you're videoes are lot worthy and helpful!!!

[@Begin_with_word]

I have no words to describe sir

[@PrinceSingh-lz7sn]

❤❤❤No sir no doubts everything is cleared . Thank you for your efforts sir . ❤❤❤

[@ng5185]

Sir in the last sum we have one remaining r for which answer is 0 but also sin(1/rcos thita) comes for this r it will be infinite . So only for remaining r it is 0 or there is any role of infinity

[@kanhiyajoshi5346]

Sir saying honestly itni videos s y umeed na rakhe ki views aache aayenge kuki is desh m bache vines dekhte h padhai ka video nhi BTW thanku sir your style is so good for explanation of tricks

[@ajaytailor2832]

Thankyou so much sir..the explanation is extremely great🤩🤩

[@vanshikapandey2432]

Your explanation is great sir 👌🏻

[@LapCreativeStudio]

hey can u help a little sir ne last question mein differentiability check kerne keliye pahele continuity check q nhi kiye ?

[@sunilbishnoi3496]

Aise feel ho rha hai ki sir ap mgsu ke privous year ke paper solve kra rhe ho Thanks sir

[@UttamKumar-jz8oj]

Sir please upload videos in group theory

[@DrVineetaNegiMaths]

I have uploaded videos on this topic.

[@ShilpaKumari-pv7wo]

Nice explanation sir 👌👌👍

[@durgeshkanathe3715]

Sir last question me fx and fy ki value 1 aayegi ?????

[@sumalyamukherjee3166]

mere bhi 1 aaye

[@arjunnagarkoti2758]

Sir, it is a necessary condition such that when numerator and denominator both degree same then we apply y=Mx? Give answer

[@udattam]

If they are of same degree, you can eliminate the variable and make the value dependent on m. So it is a necessary condition

[@sajidmunir560]

Dear sir limit (h,k) approach (0,0) f(a+h,b+k)-f(a,b)-hfx(a,b)-kfy(a,b)/√h^2+k^2 exist ki jaga equal 0 correct nhi Q k Taylor theorem or Young's theorem k proof Mai helpful ho gye

[@NeetishSahu]

best teacher sir

[@dipeshkumarsahu8600]

thanks..mor helpfull video

[@farhankhan2493]

Great 🙏

[@navjotzsingh]

Thnx ❤️sir

[@sajidmunir560]

Nice sir explain differential or error in two variables

[@Laxmisingh8491]

Sir BSc ke liye v bahut important hai ye v bol diya kriye ...❤️

[@vikass310]

Thank-you so much sir. Really you are teaching so excellent ❣️.

[@khushboo5795]

U are so helping sir

[@indrabhuarya6521]

Super Lecture 👌

[@BTEEEAbhinayGautam]

thank you sir for this great lectures it was agreat help

[@Ms_khatrifromhills]

Sir value of fx(0,0) and Fy ? Should be equal? Or we just we have to find them that's all

[@dalitshiv834]

Donno ko alag alag HAR barr Find karna padega

[@4hostelboys]

Sir Really genius... kindly upload about Graph theory

[@NRP019]

Tysm sir you are really genius hats off 🙏

[@anuragvimalverma1234]

In last question..at @19:25 if value is not 0 , but exist. ..then function will differentiable or not???

[@tejveersingh6148]

Sir our bsc exams are at our hands so please start discreat mathematics for bsc1st year 🙏🙏🙏🙏🙏🙏🙏🙏

[@rajasthani2.02]

Sir ji kya 3D geometry bsc ke lecture upload nahi he

[@AbhishekKumar-tg1tk]

thanks, sir for this amazing video

[@sanidhyakhandelwal5560]

mujhe bilkul smj nhi aaya tha mere college me sir aapone padhya toh sab aagya maine mere college collegues sab ko yahi se padhne ka recommendation diya hai thanks alot for ur kind help....hope ur channeel touch miles thank u sir

[@sunilsahani311]

Sir statics and dynamic par video upload kre plz sir exam aane wala h

[@ourcity6122]

Was waiting for it

[@suryashiskrmandal1435]

yeah..me too!!!!...Btw who r u????

[@ojashavsinghsengar3405]

Sir please upload video on schwarz and young theorem

[@kumarsantosh4499]

Nice explanation! Thanks sir

[@naveenchandpandey1486]

Sar aap mechanics ke video banae Hain

[@janashraita4194]

ThanQ sir

[@mayankag2277]

1 doubt sir.. Last question me (sin(1/h)) /(1/h) wali property lgegi toh fx( 0,0) and fy(0, 0) dono 1 aaega.

[@harshmishra5869]

Same doubt

[@ravibadwar2002]

Sir jo aapne sabse last sin1/x vala question kiya usme continuity check kaise kre plzz tell me sir humble request

[@RajatNarang]

Sir "solid geometry" ki videos aap kab sai dalai gai......... 🙏🙏please video banaia......

[@Manish-ge6cp]

Very well explained !

[@ajeet8756]

Thanks sir ❤️

[@dikshacookinghub1414]

can anyone help me that in 2nd question the value is 1 and -1 so how they exist?

[@pruthvirajcreation]

Thanks sir🥰🥰

[@goraa2425]

Thnqu sooo much sir...

[@alishasiddiqui3694]

Sir pls make a video for reduction formula intrigation for bsc plssss

[@ex-w1b]

Alisha Plz Search " Reduction Formula MKS Tutorials... Very good content😊

[@jogeshcms6639]

Great sir

[@ritikachauhan8609]

Sir quadrature pe bhi video bnaiye

[@Priyanshi_yadav928]

Exam aa gye kya sis

[@shivamkumar-vx8or]

Sir please aap funtion of three variable ki limit continuity and differentibility bi upload krenge....??????

[@armaan5275]

Sir aapne first question me limit existance ko proof nahi kiya Kuch paths ke along limit exists kr rhi hai iska mtlb ye nahi hai kinlimit exists kr rahi hai Vo aapko Epsilon-delta se proof krna pdega

[@pawan-meena]

Nice✔️

[@lfc1258]

Thnx sir ji

[@bssoni-mm5yk]

Thank you very much sir for this video. Please upload more videos on higher calculas.

[@DrVineetaNegiMaths]

I have uploaded interactive videos on the topic.

[@ffeditz_]

Sir agar limits unit nhi aarhi to limit exist karti hai kya?

[@LapCreativeStudio]

sir last question mein aapne differentiablity show kerne keliye continuity check q nhi kiya sir plz replyy

[@bikrambose4964]

Thanks sir🤘

[@kohathaddanki9844]

10:45 it's limit is not unique ka matlab kya hai? Pls tell me

[@anuragverma889]

Swarchz theorem PR aapne vdo banaya h kya?

[@mydream6751]

Sir plezzz net jrf ke liye partial differential ke lectures ke video upload kijiye😊😊😊😊

[@bablusharma7302]

Sir real analysis par video bhee upload karo na sir .

[@DrVineetaNegiMaths]

I have uploaded interactive videos on the topic.

[@aishwarya1895]

Thanks sir

[@devanshverma3017]

Sir, please make video on ERROR &. APPROXIMATION topic of partial differentiation