Taylor Series | Taylor Theorem | Proof & Series Expansion | Part-I

[@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

[@Akashalomiitbombay]

Very very nice sir

[@sachinupreti7159]

Tan inverse pi by four one kabse hone lag gaya sir ?

[@sachinupreti7159]

Go threw yur video and check it ,. 🤖🤖

[@nailawaqar362]

Thanks a lot Sir 👌

[@mariyanizami4904]

Sir u r amazingly superb

[@kuldeeplakheshwar7811]

India's best 'last minute savior', specially for engineering students 😁.

[@che-17pratichishukla83]

Yes bro😅

[@souravdandapat4361]

@@che-17pratichishukla83 kal exam hain
😁

[@nehasharma-fe5gn]

Actually 😂😂😂😂

[@CS__ADITYASHRIVASTAVA]

@@nehasharma-fe5gn Are you an AKTU student 😂😂?

[@HarmonyBlend]

Yes bhai such kh rha hai

[@sirivennela2260]

I scored 28/30 just by seeing ur video in UA-cam abt tracing of curve and radius of curvature.. Thank u soo much sir

[@yubrajkarki.]

u scored 28 marks in final exam or internal exams

[@CaptureMatrix]

mid sems ??

[@niteshrajak6236]

In 2nd question of Taylor's expansion you take tan in the place of tan^-1(tan inverse) at the time of placing values (pi/4).

[@bloodynoobsnip3420]

Because tan inverse pi/4=1 hota h

[@rujulasingh1870]

@@bloodynoobsnip3420 tan pi/4 =1 hota hai

[@bloodynoobsnip3420]

@@rujulasingh1870 sorry sorry may be it was a mistake

[@hallo_Deutsche]

i had the same doubt

[@uniqueness0037]

Non guys tan^-1= π/ 4

[@shreyanshtiwari2366]

Who is here before 1 day of exam ?😊😊😊😊

[@gauravthakur6873]

Me 😂

[@baldevsharma626]

I am here just 1 hour before exam

[@brownmunde7844]

Mai bhai mai

[@shreyanshtiwari2366]

😁😁

[@Mr.MRBmathematics]

I am also bro

[@AS-dq1ku]

Sir the best part of you that you don't make any video longer....
That helps me to complete any topic in just few minutes... 😊
Thanks sir.. ❤️

[@shreyaskulkarni6910]

2 waqt ki roti rehane ke liye ghar aur maths me pass hone ke liye Purohit sir aur kya chahiye jine ke liye, hats off to ur work sir, great fan of yours 🙏🏻🙏🏻🙏🏻🙏🏻

[@informalpivots7673]

Normal student is learning online now from school and
Pros are learning from here
Thank u sir ❤️

[@PriyanshuBhalla0]

THANK YOU VERY MUCH SIR.... WITHOUT THIS I WOULD HARDLY PASS MY MATHS EXAM...YOU ARE BLESSING FOR US❤️

[@jasobantadas4945]

11:47 thats tan ^ -1(pi/4) and it is not equal to 1
Thank a lot for ur efforts sir

[@manpreetkaur1757]

@@cinemann7 no..tan inverse ,,its not like u r saying it..its value cannot be one

[@adityamajumder2689]

@@cinemann7 bhaisaab whole inverse mein hota h

[@shrantsiddhe]

Yes

[@gourprashant1525]

Sir aap ka concept bahut acchhe se samajh aata hai

[@kaustubhpaturi4801]

While watching this video, I realised that my right ear is deaf...
But the explanation is really very clear. The way you teach, I feel like skipping college math classes and learn from your videos.
Thank you so much sir!!

[@bemoreawesome8955]

How did you came to know that your right year is deaf

[@saakshi5823]

Sir, in the tan x question, f(pie/4), will not be 1 because the range of the Tan inverse function is (-pie/2,pie/2) hence it should be written as it is tan inverse pie/4...... btw good videos

[@RahulKumar-nd2sp]

Yeah, I also noticed the same

[@AnkitGupta-ix3st]

Yes, I've noticed this🙂

[@sarthakjain5084]

I was looking for someone in the comments to pinpoint this mistake nd i found u cutie

[@sonamsonam4824]

Sir m to Puri MSc maths aapse hi padh rahi hu or mujhe benefit bhi ho raha hai ❤❤ sir aap bahut acha padhate ho bhagwan aapko lambi Umar de or aap khush raho always ❤❤❤❤❤❤❤

[@vaibhavkaushik627]

Sir,you are doing a great job. I wish for your prosperity.May every God blesss. You videos are very good are help me a lot.Stay motivatedd and be happy.

[@MarufKhan-sm6ln]

My favourite teacher, love u sir ❤️❤️❤️

[@yoursheartbeats5906]

Same same

[@crazyhumi1321]

Mine too

[@shreyakumari9616]

Sir please make videos on hyperbolic and inverse hyperbolic functions also..
Ur videos are really helpful sir..ur efforts are really excellent sir...

[@zenerywei2178]

Big Thanks to you sir Gajendra🙏
May god bless your Life 💗

[@oreawajojoda]

sir, in the question 2 there is mistake tan-1(pie/4) is not possible
so change the question as,
expand tan-1x to the power of (x-1)

[@bishnumadkami6453]

I am very happy for your teaching sir .thank you so much sir

[@pratyushraj3393]

You made this topic very much easy to understand. Thank you sir🙏🏻🙏🏻

[@deepakkumarkapri902]

Sir, aap bahut accha kar rahe hain , tution se achcha To aap padha lete hain aap aise hi padhte rahe ham log ko hum Bhagwan se yehi dua karenge ki aap lambe samay Tak jiye aur aap students ko madad Karen thank you very much sir

[@khushalkhangharani9394]

Nimasty Sir! Sir your way of teaching is appreciable God Bless you💗

[@masterdementer]

11:50 Tan inverse (π/4) is not 1. Tan(π/4)=1. Since its in radians and we are taking inverse I dont think its possible to get the value for that, even tan inverse calculator returned null

[@aalokbhanot08]

great effort on your part sir. it really helps a lot during exams. you have covered the whole syllabus in a very systematic way and it is very useful to understand the concept easily😊

[@adarshsingh8464]

thank you sir for uploading such as wonderful videos, after understanding theorem and solving example i had solved all questions my book,please upload videos on bsc 2nd year mathematics

[@b30luvkumar52]

sir you are god to me , teachers like you are reason why im topping my college .

[@jagdevsingh6714]

From which state ❓

[@vinodbamniya6872]

Sir aapke video se muje help Mili aur mene class me maths me second position hasil ki ....... Aap concept aache se explain krke questions smjhate hoo ....
Thank you so much sir

[@bhaskarainam7672]

Gajendra sir u r really last minute savior 🔥🔥

[@Unkown4685]

Thank you Soo much sir... I passed my M1 by referring ur vdos within 3 days... Basically I'm a lateral entry student to engineering Soo they haven't teach m1 properly Soo I have referred ur vdos before 3 days... Finally I have passed ❤️ thank you sir 👍🙏

[@cvrcollege9552]

THANK YOU SIR, You saved me from failing in tomorrow examination
Now I am confident.
Thankyou so much sir...
Sir,I have watched sequences and series,multivariate calculus and univariate calculus
Far better than my lecturer.........
Good examples too...
👌👌👌👌👌👌👌👌👌👌👌👌👌👌👌👌Thankyou so much sir..

[@RAMKUMAR-ni8uw]

very helpfull lecture sir greatest mathematics channel ever i have seen ..... so respect sir

[@hrt1327]

At 8:04, why did he take f(2+x-2) anyone?

[@prowlawsm]

begins AT 1:52

[@RahulKumar-hq6wm]

Sir thank you for all of this what you are doing to us......😊😊😊😊
I am a kind of poor in maths but your lectures are really helpful to me.

[@yubrajkarki.]

u are poor and very poor in mathematics

[@satyamppps]

Awesome sir.
I am also a physics teacher at kota.
I am studying mathematics for my gate paper.
U r just awesome.

[@ajonson758]

If you are physics teacher at kota then i am maths professor of Stanford University 🤣
Just kidding Don't mind 😃😊

[@sauravsharma4028]

I m studying ur videos sir for LT exam
Thank u so much sir

[@Yash123-c9g]

Thanks a lot sir,just viewing it 1day before my externals but I totally understand it.

[@pavanajsridhar939]

sir, you are awesome! But mathematics is all about proofs. There are very few proofs of theorem in your channel and plenty of problems to ace any exam.But I am sure there are math lovers who are ready to learn extensive proofs of various theorems especially from an awesome teacher like you sir. Therefore , I request you to make more conceptional videos with proofs rather than mere statements and assumptions .

[@DC-zi6se]

I think this is more for Phyiscs, Stat and Engineering students. Rather than pure math.

[@shubhtrivedi19]

I have understood it clearly. Thank you sir so much 🙏🏻🙏🏻

[@vandanachauhan4578]

Your videos are really nice sir your way of learning is appreciable

[@melodyvibescanorous]

We are grateful that we have such top level mentorship. Concepts have been made so easy to understand.
Worth learning!!

[@hacker_subbu]

Anyone here from btech 1st year 2023 batch❤😊

[@niteshsharma7945]

Yes

[@savanpatel7118]

Sir I’m from NIT and really you are teaching as same as my teacher in NIT
Apako to IIT/NIT me hona chahiye....!!!

[@abhinavsinghtawar9157]

I was also going to write the same comment

[@abhinavsinghtawar9157]

@@adarshanand3724 which IIT , mine is IIT Jodhpur

[@imuv1008]

Taylor Swift❌ Taylor series✅

[@techstudent351]

13:23 yha 1 kaise hua jb f(x)= tan-¹ x
Then f(π/4)=tan-¹π\4 hoga na.... please clear this problem.

[@ELBMohdUsman]

Thank you very much sir🙂 .Your teaching style is magnificent⭐.
Keep doing this awesome work.
We love you sir.

[@Sageerahamedkhan]

Are sir g maine to phli bar apka video dekha h aj
Ksm se sir g mja aaa gya
Thank you very much sir

[@Sportsenthusiasmsupporters]

Sir I would like to apologize to you you are great but in 13:44 sir tanπ/4 =1 but tan inverse π/4 not equal to 1

[@something7419]

exactly

[@Navneet_100]

Oh bro understand the concept not the calculations. Sir's main focus is to teach concept and calculations mistakes are just silly one can neglect it.

[@ashleystephen7365]

@@Navneet_100 Tell that to my Maths Teacher

[@Navneet_100]

@@ashleystephen7365 You are not a school going student .
Knowing concept and not implementing it , will lead to silly calculation mistakes only.

[@saikiranchowdary7376]

@@Navneet_100 All r imp bro

[@pritpatel9938]

00:01 Taylor series expansion is used to expand a function at a particular point.
01:33 Understanding Taylor Series and its theorem
03:29 Calculus derivative is used to calculate Taylor series
06:08 Taylor Series and Maclaurin Series are connected.
08:23 Taylor series is used to approximate functions using polynomial expansions.
11:06 Taylor series is a mathematical approximation method
13:58 Introduction to a new theorem and its application
16:37 This video is part of a series on Taylor series and there will be more content in the next video.

[@nishantpatel6755]

Thanks sir ❤️
But sir last question can also be solved like--. Taking "log x " in LHS and then by property we can write log(1+x/h)and then use expansion we can get the result.🙂

[@chandlervikramsingh5985]

No babes can't do that way

[@bhaveshvsv8167]

Where are you from bro

[@chitratechnical5893]

Sir tan^(-1)π/4 isn't equal to 1.11:50

[@abhiseksahoo7491]

Sir here in one question you've used tan-1(π/4)=1. But it's wrong. But rest of the class is very helpful for me. Thank you sir for uploading such type of videos 👍

[@chandlervikramsingh5985]

To kya hota hai chu

[@NHCEHarshitTiwary]

Bhai tan inverse(π/4) 38.14 hota hai

[@chandlervikramsingh5985]

@@NHCEHarshitTiwary sorry bro bhawanaon me beh gaya the notice Nahi kiya ye tan inverse tha

[@chandlervikramsingh5985]

@@NHCEHarshitTiwary 😂😂

[@NHCEHarshitTiwary]

@@chandlervikramsingh5985 😂😂😂 lol

[@Iimian.....123]

India's best last minute saviour for bsc students 😅

[@MukundJainBCL]

sir in second question you have made a mistake in putting the value of pi/4 it should be 1 in place of pi/4 but its great video thank u

[@manishdev8695]

Mujhe apka sara video smjh me aa jata hai
Thanks you sir for our mentor 🙏🙏🙏

[@mdnasifmahmudzishan7032]

Sir your videos are just too good and helpful !!!!

[@divyeshshethna7502]

Sie, you are really doing fabuloas job. I just request you to upload all videos covering all topics of Mathematics soon.

[@envfamily9938]

Thank you so much sir....it really helped me a lot for last minute preparation 🙂🙂

[@Nidhi-Dodiya-1014]

11:52 tan inverse pi/4 is not 1.

[@MithleshKumar-yy3fe]

Sr after solution u gives some questions related to theorems ,,,, because we can solve the problem ,,,,,,,,
And plz provide any reference book preparation for BPSC and UPSC for mathematics

[@y016archisprabhughate7]

Sir , at 11:51 arctan(pi/4) = (0.666)radians (please check) and Thank you sir for making amazing videos.

[@programmingwitheddie9791]

Yes I also found this same mistake...

[@ghungrubella9043]

Yaa broo he did wrong tan inverse of pi / 4 is not 1

[@purnimamondol5979]

Thank you so much sir. Its really helpful.
Grateful to you sir 🙏❤

[@RoshanKumar-gp5hu]

Sir your teaching method is too good really sir please jada short karke ni padhaiye kahi kahi confusion ho jata h, by the way I have no words to say u sir thank you so much

[@lalitasingh9698]

Tomorow is my maths sessional and here i am . 3 more unit to go haha

[@ShivaKumar-to6lp]

Sir apki video meri bahut help krti h

[@rohitjaiswal8601]

Thanks a lot sir for all these wonderful content

[@Muhammadkashif-kg5sw]

Good sir
Your video help me

[@sumanranjanpujari7871]

Sir Taylor theorem cauchy form of remainder yeah bhi chahiye

[@vaibhavdhiman8317]

The peoples who are watching just in 1 night before their exam >>>> legends 👍:)

[@Celebrity_arpit]

Sir your contents are really helpful for mathematics exam,😍😍Thank you Sir for your precious time😇

[@NikhilChauhan-o9c]

Before college nexa classes and now sir you ❤❤❤

[@Captain-7-7]

Ha bhai 😅

[@janvijpatel219]

Greetings sir !! You have a great energy. Your videos are helping me a lot in my preperations😇 you are doing great sir thank you so much 😇

[@DineshSharma-ee9qs]

Janvi Patel ji aapki aakhe mregnaini jaisi h yaar mainbloig

[@babloo4423]

Same

[@POOJASINGH-hd5qi]

Sir aapke samjhane ka tarika bahut acha h mai bhi aise hi samjhti hu pahle example solve krke fir theory

[@imranomar207]

Dear Sir Great job keep it up

[@mohdriyaz1060]

Awesome and very nice video thank you sir 👌👌👌😃😃😃👍👍👍

[@niharikakapil5759]

Really helpful video sir...keep making these videos ❤️

[@simranmahendru2910]

Best teacher ever

[@krishkakadiya8724]

hi

[@debjeetdas_0687]

very helpfull sir...ur way of explanation is just amazing..

[@rocky-themonster7874]

11:50
tan inverse he na 1 thodi ayega 👍

[@HarshKhatnavliya]

Who is here before 2-3 hours before exam 💀

[@utkarshpandey8967]

Thank you very much sir for putting this much effort for us.

[@kdknowledge7453]

Very nice work sir iam student of bsc 1 year tis video is very helpful

[@apangshude2773]

Video starts on 1:52 sec😊😊😊

[@simviii_1120]

Very nyc way of teaching 🙏

[@GaganpreetSingh-ft1xi]

Sir , u r really doing well👍💯
Keep it up . ❤️❤️

[@yubrajkarki.]

sir ko keep it up bol ta hai he is very eduacted lecturer and professor samjha tu unke samne piddu hai chota sa nanha sa bachaa ache sey padae kar samja bada aya keep it up bolne wala chachundar k bachhe

[@TechWithSurya]

Sir, End Moment Par Bacha Liya Aapne Tnxx trillions of time

[@lordbeerus4546]

11:50
There's a mistake

[@dhruvsingh34]

Yes tan(pi/4) = 1
But arctan(pi/4) ≠ 1
But mistakes happen. 🤗

[@thisisvishalpandey]

Human error 101

[@abidhossain3570]

Super helpful sir. Thanks a lot....I'm from Bangladesh. It helped me a lot before my exam.

[@theycallmedinesh]

Sir 11:50 par fx =tan inverse x h wha value 1 nhi aayegi

[@biharboardscience]

Yes

[@RameshTomar-y4w]

Very very thank you so much sir aapke ki halp se mujhe aadhi maths aa gyi he I'm engineering student

[@ruovinuousou2163]

Sir, What is the difference between Taylor's series and Taylor's theorem?

[@tahiyatarannum7016]

your lecture really helps us. Thank you very much

[@Manish-bs4mh]

Thank you sir for sharing this idea with me. God bless you!

[@Rishi_Mandloi]

Tomorrow is my exam.....I started my syllabus today
Hope I will pass🙂

[@debashiskar8970]

sir, tan^-1(pi/4)=1 kayse huya ? [2nd problem main]

[@user-mx1hm7ju8q]

mistaken, more mistakes done as well

[@sonamsonam4824]

Best maths teacher in the world ❤❤

[@anshulsharma1594]

Today is my exam so i am here 😅

[@madhav6248]

Sir you are the best teacher of higher maths sir please keep doing our help sir

[@lefthooklarry6983]

Your videos have helped me immensely in passing maths 3 . Thanks a lot sir🙏