One correction on the DEC 2023 question : on 52:30 h(x) = x² is not uniform continuous on [0, ∞) hence the 4th option will be discarded. Sir, himself has mentioned it's not UC on the next question. Its not UC because we have two sequences aₙ=√(n+1) and bₙ= √n on [0,∞) such that |aₙ - bₙ|---> 0 as n--->∞ but |f(aₙ) - f(bₙ)|---> 1
Very useful and understandable sir. Thank you so much sir. I have not qualified NET since 4times next time. Your lectures are so helpful and i have to attempt this December
Thank you so much sir ❤ you solve csir question like board exam questions you have great skills to solve problems and you teach us for free . thanks again ❤
Its my humble request to all the aspirants to kindly like the video too it would take just 2 seconds, but it would benefit the reach of this video thru YT algorithm. PS: despite 4.2k views only 200 something likes is non-reciprocation of sir's efforts!!
Sir my another request, can you solve csir problems on singularity topic in complex analysis with short cuts. After completing differentiability topic in real analysis , as these series are very useful for our last minute preparation for csir exam.
Answer for the last Question - a) is wrong because f and g are u.c so both are bounded. b) is wrong from last two options we conclude that it may not be closed so may not be compact.
4.4k watch n why you are guys not liking the vedios ? I don't think anyone can explain here on yt history even i went to dips their questions discussions was in the air they didnt wait cz they taught iitians n DU students who were already toppers I never gets why they take choching even after coming from institutions like that. Well its humble request to all of you who are attending lectures series here to like the vedios n share too
Thankyou for this lecture Harish sir, with these videos we are able to analyse that csir is just repeating similar qns year after year. Your approach makes the csir look doable busting all the myths prevailing in Delhi based coachings. PS: sound issue is still prevailing, kindly look into it. As this problem ruins the quality content that you're delivering in lecture.
Last question, option b is also correct because if I is compact ( closed and bounded) then f and g are both bounded and hence fg is uniformly continuous
Sir I have a doubt in 44:42 ... According to your shortcut, in option c, f(g(x)) g(x) is uniform continuous, but f(x) is un bounded so f(gx) cannot be uniformly continuous. How can I differentiate option 1 and 3?... Please clarify sir... Thankyou ❤
Thankyou sir. The session was awesome. I know you are proficient in this field. Sir please check it according to official answer key correct answers for the question (53:00) in 1,2 and 3, forth one is incorrect. Once again thank you.
53:20 in this question it was asked that which of the following options implies that the function f is UC, it is not already given UC, which you told so :(
For the last question. Option a Since f,g are UC therefore both are bounded. So either f or g us bounded is wrong. So option a is wrong. Option b If we choose I as Real numbers then it is not compact. So option b is also wrong. Is it right sir??...
@@king-by1kh Bro h is defined from I to R ...so we need to consider an interval in which f and g are u.c that's why interval must be bounded for h(x) to be u.c.
Your lecture series is make us strong to fight any exam within suitable time
One correction on the DEC 2023 question :
on 52:30 h(x) = x² is not uniform continuous on
[0, ∞) hence the 4th option will be discarded. Sir, himself has mentioned it's not UC on the next question.
Its not UC because we have two sequences aₙ=√(n+1) and bₙ= √n on [0,∞) such that |aₙ - bₙ|---> 0 as n--->∞ but |f(aₙ) - f(bₙ)|---> 1
U r right 4 th option is not correct..!!
great lecture with very useful shortcut methods, thank you sir
Very useful and understandable sir. Thank you so much sir. I have not qualified NET since 4times next time. Your lectures are so helpful and i have to attempt this December
Thank you sir for providing this lecture
Sir your approach to Csir net Questions is Always Unique...
❤❤❤
Thank you so much sir this is too much helpful and exam so near thanks again
Very help full lecture for preparing net, I shared it among my students preparing net . thanks sir
Thank you so much 🙏 dear respected sir 🙏💖
Thanks alot Sir
Thank you so much sir ❤ you solve csir question like board exam questions you have great skills to solve problems and you teach us for free . thanks again ❤
Its my humble request to all the aspirants to kindly like the video too it would take just 2 seconds, but it would benefit the reach of this video thru YT algorithm.
PS: despite 4.2k views only 200 something likes is non-reciprocation of sir's efforts!!
THANKS YOU SIR FOR THE LECTURE IN UNIFORM CONTINUITY 🙏🙏
Thank you sir ❤
Sir my another request, can you solve csir problems on singularity topic in complex analysis with short cuts. After completing differentiability topic in real analysis , as these series are very useful for our last minute preparation for csir exam.
Thank you ❤
Superb session.....❤
Very. Very helpful❤❤❤❤
Thnku so much sir its really helpful 😊
I am really happy sir ... I understand all concepts easily
Thnaku sir apke video se ese lgta h jse csir easy h
I must say your analysis is so strong 🙌
Differentiability ke baad complex analysis (bilinear transformation) ka topic Kara dijiye sir
34:46 plz check
25:05 sin and cos function always continuous at (0,2pi ) so why not Continuous 😢
Sir your video lectures are very helpful
Answer for the last Question -
a) is wrong because f and g are u.c so both are bounded.
b) is wrong from last two options we conclude that it may not be closed so may not be compact.
very helpful👌
1:07:06 d option only correct
Yes
very helpful
Thanks a lot sir
Thank you for more supporting sir 🙏🏻♥️
Your service for us will be remember for ever ❤❤
4.4k watch n why you are guys not liking the vedios ? I don't think anyone can explain here on yt history even i went to dips their questions discussions was in the air they didnt wait cz they taught iitians n DU students who were already toppers I never gets why they take choching even after coming from institutions like that.
Well its humble request to all of you who are attending lectures series here to like the vedios n share too
Thanks a lot sir ❤
Thankyou for this lecture Harish sir, with these videos we are able to analyse that csir is just repeating similar qns year after year. Your approach makes the csir look doable busting all the myths prevailing in Delhi based coachings.
PS: sound issue is still prevailing, kindly look into it. As this problem ruins the quality content that you're delivering in lecture.
Charan sparsh Gurudev....
Thank you so much sir ❤
Last question, option b is also correct because if I is compact ( closed and bounded) then f and g are both bounded and hence fg is uniformly continuous
No
50:05, last option doesn't seem correct because then f will also be uniformly continuous.
Thank you sir
Sir I have a doubt in 44:42 ... According to your shortcut, in option c, f(g(x)) g(x) is uniform continuous, but f(x) is un bounded so f(gx) cannot be uniformly continuous.
How can I differentiate option 1 and 3?... Please clarify sir... Thankyou ❤
if that condition holds that only gurantees that..if it not then you can't say anything...apply derivative test
@@dhrubajotidas8276 Ok thank you
Thankyou sir. The session was awesome. I know you are proficient in this field. Sir please check it according to official answer key correct answers for the question (53:00) in 1,2 and 3, forth one is incorrect. Once again thank you.
Again thanks sir,
Sir please make a video on Statistical Inference
53:20 in this question it was asked that which of the following options implies that the function f is UC, it is not already given UC, which you told so :(
Thanks Sir❤
🎉 thanks sir
nice sir
Sir please upload sequence and series of function pyq video
Already uploaded.... Check my lecture "Uniform Convergence"
ua-cam.com/video/Qi4cDKUCGmI/v-deo.html
This is the link
Okk sir . Thank you sir 🙏🙏
Thanku you sir❣️🚩
For the last question, By Heine Borel theorem, I is not compact since option(d) is discarded.
52:00 Last option is incorrect as x^2 is not uc in R, its graph is parallel to Y axis
Ya I have the same confusion
Thanks sir
For the last question.
Option a
Since f,g are UC therefore both are bounded. So either f or g us bounded is wrong. So option a is wrong.
Option b
If we choose I as Real numbers then it is not compact. So option b is also wrong.
Is it right sir??...
real number is not an interval
@@dhrubajotidas8276 It is an interval
1:03, f is uniformly continuous doesn't imply f satisfies lipchitz condition
UC=> lip. But converse need not to be true
Converse is true only if derivative is bounded
Kindly provide lecture on abstract algebra also.
Kitne bar bole.. Sit ka domain nahi hbye subject
25:38 que ka ans shi lga kya sbko ...?? f(2π) ki value galat h ..mere hisab s to c option shi hona chahiye ...anyone correct me if m wrong
galat hya woh
Yes 👍
tysm
Sir tifr ke last two three years ke real and linear ke questions bhi krwa do if you have time tifr concept are repeate in csir I think . thanks ❤
Great 🙏 .. Some mistake I think in ques. Gate 2004?
Sir f(x) =x and g(x) =1 then clearly h(x) is Uniform continuous on R clearly R is not bounded so how option c is true only option 1 is true sir
given I is an interval
@@dhrubajotidas8276 R is also an interval (-infinity, infinity)
(a, infinity) is also an interval
@@Pbt656 we have to discard the option so we take R other wise it always hold on finite interval
Last question ans is option
A and C
1:07:06 up ne question ko sahi se read nhi kiya 😢
Sound quality sahi nhi h😬....
In last pyq it is not compact since not closed and option a is true b is false
How option c is true bro if f(x) =x and g(x) =1 then clearly h(x) is Uniform continous On R but R is not bounded so how it is correct
@@king-by1kh Bro h is defined from I to R ...so we need to consider an interval in which f and g are u.c that's why interval must be bounded for h(x) to be u.c.
But it is not necessary because I is also consider as(-infinity, +infinity) f(x) =x is Uniform continuous on R but R=I is not bounded
Yes opt a is crt
I ask about option c brother
A,b,c
ONLY ANSWER C IS CORRECT
🥀
B and c
ONLY ANSWE C IS CORRECT
Sir make video on NBHM pyq
Thank you sir 🙏🙏
Thank you so much sir 🙏🏻🙏🏻🙏🏻
Thanks sir ❤
Thank you Sir
Thank you sir
Thank you so much sir 😊
thank you sir
Thank you sir