Thank you Sir . You are really making mathematics easy and interesting .we appreciate your continuous hard work for us. Now we are waiting for continuity uniform continuity and differentiability .
Correction : 1. On 1:02:23 the seq. is not a decreasing seq, take + instead of - and the seq. aₙ= 1+ 1/n also goes to 1 hence option (a) will be discarded🙏 Alt approach : For the same question option (d) it's correct by Abel test for series 2. On 1:27:54 please observe the 1st and 3rd inequalities are correct but the 2nd one is wrong I think I got a counterexample for it as follows:- take aₙ= (-1)ⁿ and bₙ= - 4 constant seq.
at 38: 30 , sequence is not monotonic . it is bounded between 0 and 1. and its complimentary pair of sequences are monotonic , one is increasing , other is decreasing. therefore, seq is not monotonic . check by taking value of n
Sir your videos are very helpful to build counterexamples and shortcut tricks to solve the questions in efficient manner, moreover I recommend your videos to my friends circle who already subscribed to offline coaching but they prefer your lectures too ( a large no. of them ) ❤❤
Very useful.... Thank you sir! I'm glad to gain knowledge from your videos ❤ Sir i suggest please recheck the quality of voice in videos... In recent uploaded videos... The voice is not clear or breaking.. 😊
Sir there is a little issue with the mic. And we know it's not easy to upload vast Abstract algebra course, but can you share some important group theory tricks
THANKYOU VERYMUCH SIR.SIR PLEASE QUICK UPLOAD OTHER VIDEOS CONTINUITY ,DIFFERENTIABILITY AND UNIFORM CONTINUOUS.EXAM START ONLY TEN DAYS.SIR PLEASE QUICK VIDEOS
Great lecture for CSIR NET aspirants🎉🎉🎉🎉🎉
Thank you Sir . You are really making mathematics easy and interesting .we appreciate your continuous hard work for us. Now we are waiting for continuity uniform continuity and differentiability .
@Dr. Harish Garg .... Great Lecture... need to upload more such type... to help those who does't afford coaching ...blessings
Awesome 👍
Very helpful...
Correction :
1. On 1:02:23 the seq. is not a decreasing seq, take + instead of - and the seq.
aₙ= 1+ 1/n also goes to 1 hence option (a) will be discarded🙏
Alt approach :
For the same question option (d) it's correct by Abel test for series
2. On 1:27:54 please observe the 1st and 3rd inequalities are correct but the 2nd one is wrong I think I got a counterexample for it as follows:- take aₙ= (-1)ⁿ and bₙ= - 4 constant seq.
At 01:27:54 Option (1) and (4) are only correct option.
Third is not satisfied by all sequences.
It was great help sir thank you...
Amazing lectures🎉🎉
Thanks for your short cuts and tricks sir
😊😊😊
At 39: the sequence is not monotonic
You are magician of mathematics. Genius sir. 🙏🙏🙇🙇
Thank you so much Sir 🎉 nice explanation and really you are a great teacher❤ and your short cut tricks just like awesome 😎👍🏻👍🏻❤
You are so talented one...Love you sir ji... Hat's off to your hard work 🙏💞🙏💞 We will be grateful forever....make more videos on different topic
at 38: 30 , sequence is not monotonic . it is bounded between 0 and 1. and its complimentary pair of sequences are monotonic , one is increasing , other is decreasing. therefore, seq is not monotonic . check by taking value of n
yes x_3lies b|w x_1 and x_2 then How it can be monotonic
amazing🎉
Thank you sir ❤ 👍 you’re channel is more than sufficient
very helpful lecture
Excellent lecture, Sir
Great sir🎉
Very helpful for me
Thank you sir
Thank u so very much sir
Nice
Thanks a lot sir for all short cut tricks 🙏
Sir your videos are very helpful to build counterexamples and shortcut tricks to solve the questions in efficient manner, moreover I recommend your videos to my friends circle who already subscribed to offline coaching but they prefer your lectures too ( a large no. of them ) ❤❤
U r great sir
Thankyou sir for this lecture.. learned new tricks also got revision of infimum/supremum qns.. very helpful..
It is very useful and has knowledge of limits. Thank you so much, sir.
Great great great great 👍 sir
good job
mind blowing sir love u
Very useful.... Thank you sir!
I'm glad to gain knowledge from your videos ❤
Sir i suggest please recheck the quality of voice in videos... In recent uploaded videos... The voice is not clear or breaking.. 😊
Thank you so much sir.. I gained many information and shortcuts by your class. The classes are useful to us..... so don't stop it doing sir....
Great explanation Sir 😊
Thanks sir
Thank you Sir most awaited content.
❤❤❤
Very useful sir
Really sir your videos make any topic very easy.....
Tqsm sir❤
Great and amazing explanation sir❤❤
Sir at 52:46 if we take the function f=sinx/x at x tends to 0 it is 1 but it is not always positive
Great explanation sir... Thanks a lot...
Thaanku sir
Thanks for making this video sir
Thank you so much for this wonderful vedio
Sir bhut achha lga pdke ...plz upload next vedios we are waiting
Sir jii apka jawab nhi hai king hai aap sir jii ❤❤❤
very good explanation sir
Thanks sir...now I'm waiting for continuity and differentiability for one variable...
Thanks🙏 to you sir
Sir your explanation trick is amazing
nice sir
Very nice sir
Thank you so much sir ❤
Thankyou so much sir....😊😊
cool
Sir,
If I clear the CSIR exam it's fully because of you... Great work you are doing sir.
39:47 c,d true
Many Thanks 😇
Sir please upload videos on group theory also we need a lot for make our preparation boost
Thanku so much sir means a lot❤
Thank you sir... For making this video in English ❤...
Thank you sir ❤
Thankyou sir ❤❤
Thanks 🙏
Thank you sir
Thank you
Thanku so much sir.
Sir at time 43:00 we use cauchy 2nd theorem..?
Thank sir
Dedicated teacher
Thanku so much sir
Thanku sir ❤
Thankyou sir
Tq sir ❤
38:12 a option not true please check it
Non monotone hoga vo
X3 lies between x1 and x2
@@soniyakundan1891 okk
Sir there is a little issue with the mic.
And we know it's not easy to upload vast Abstract algebra course, but can you share some important group theory tricks
38 subsequence monotone but sequence not monotone
3 and 4 option correct
Please upload continuity uniform continuity and differentiability
Thanku sir
THANKYOU VERYMUCH SIR.SIR PLEASE QUICK UPLOAD OTHER VIDEOS CONTINUITY ,DIFFERENTIABILITY AND UNIFORM CONTINUOUS.EXAM START ONLY TEN DAYS.SIR PLEASE QUICK VIDEOS
I am waiting you're lectures sir.
Sir abstract algebra(group,ring,field) ke upar bhi ek pyq video kijiye na...
Can I use ratio test at 43.12
Eagerly waiting Indian Statistical service Previous Years Questions
❤❤
Sir abstract algebra k pyq bhi solve krwa do
Sir can you also provide lecture notes
🎉🎉🎉🎉🙇🙇
I got confidence to Crack CSIR NET and KSET
Sir measure theory ka pyq solve karwa dijiye
1:29:07 check example not valid ❤
Group Theory lecture
Audio is sometimes not enough sound sir... 😢...
voice😮😮
Pls large size
Determinant pyq
Great 👍 sir
In this video is voice problem 😢
Sometimes sound problem...😢
46:pe sir shydd aapp galata aise koi theoram naii hai
Sound quality kya hogaya h.....bht dikkat ho rhi h