I went to many institutions and invested a lot of money 💵 but no one ☝️ taught like you …..and you taught so very well 👌 without any fees thank you so much dear sir ❤

@yogendravishwakarma5592

Ай бұрын

Forget wrong things only take right and good things.

@sheemanitinsan7235

Ай бұрын

@@yogendravishwakarma5592yes ♥️

@aakashbhuse3170

Ай бұрын

Because he is recognised by the top Indian scientist in the current time and recently included in the top 2% scientists in the world !!

@sheemanitinsan7235

Ай бұрын

@@aakashbhuse3170 absolutely 💯 right brother

@Dr.Harish garg , at 1:16:37 csir net June 2019 . Sir In this problem options (c) and (d) are also correct.

Superb session.....❤

Thankuuu so much sir.your teaching style is excellent.❤❤❤❤❤❤❤kash ap hmee phle

very helpful sir `thankyou so much sir .

Very helpful sir . Please upload more videos.

My prayers and wishes are always for you sir 🙏

Very helpful ❤

Tku sir Your videos very use full sir

Bahut jyada helpful h sir ji

Aisa content aaj tak nhi mila you tube pe... difficult topic hai isko banane ke liye bhot thankyou sir... kindly make topicwise aptitude pyq

Sir this is very helpful please upload next 2 lecture very soon please your trick very helpful in exam

Really, you are teaching Real analysis, sir; thank you so much for sharing such videos.

Very nice lecture sir....

at 35:40 how did we have discarded the unbounded option(d) .Please provide a valid justification for the same

@dipeshvishwakarma3511

Ай бұрын

1/1+e^x is cts, one one and bdd.

Thank you so much sir 🙏🏻🙏🏻🙏🏻

Thank you so much sir ❤

Very nice explanation, thanks sir

Thanku sir

Thank you for your efforts sir 🙏

Very helpful 🎉🎉🎉

Thank you sir😊

Really you are great sir ❤

Thanks again ❤

37:10 how can we consider A=R in the (4) option sinceR is not compact

@newsteplaiddown9481

Ай бұрын

A={1} it is compact , f^-1({1})=R it is not compact

Thank you sir 🙏

Thank you❤ sir

@ dr harishgarg 41:00...a option kaise shi ho gya ...f(a ) bdd to a ko bdd kaise bol skte h ..inverse image thode hi bdd hoti h

Thanks sir...❤

You are genius sir

Please complete this topic with uniform continuity and all

@DrHarishGarg

11 күн бұрын

Already uploaded.... See at my youtube channel.

Thanks a lot sir jee .

solid content sir

37:24 can anyone tell me..why sir had not taken compact subset A...why he has taken A=R

@Dearbhanusir

Ай бұрын

Yes A can't take R because A is compact

Please explain in bilingual. Your lecture is very useful for me. Thanks sir

Thank you sir

Thanks sir ji

love you sir❤❤❤

Thank u sir ❤️❤️❤️❤️

@50:14 option (d) is incorrect as compact set will map to compact set. Is this correct or not? Can someone confirm?

Thankyou sir

sir last request..... please upload a video on pyqs of ring theory.... 🙏🙏

Thankyou

Thanku sir❤

Sir please upload the vedios of linear algebra ... inner product spaces...and orthogonal...invariant subspcaes...

@DrHarishGarg

Ай бұрын

Linear algebra, inner product space etc already uploaded.. Explore at my youtube channel.

@kalyandasguruji

Ай бұрын

@@DrHarishGarg ok sir thanku

Please upload the next lecture,

Sir... Please... Which software you are using for screen recording this video ?

Thank you sir🙏 Sir at 43:04 image of close interval under countinous function is always closed. and range of tan ^-1x is -pi/2 to pi/2 . So how option 1 is incorrect

@Siyagupta52

Ай бұрын

Take f(x)=e^x , A=R then f(A)=(0,oo) which is not closed

@shefalithakur4580

Ай бұрын

​@@Siyagupta52 ha to in this case you take A=R which is not closed But continuous function always map closed to closed Compact to compact Cauchy to cauchy So option 1 is true here

@Siyagupta52

Ай бұрын

​@@shefalithakur4580continuous function maps compact to compact Closed to closed is not true . As take the same example of e^x

@shefalithakur4580

Ай бұрын

@@Siyagupta52 I got it dear thanks Continuous not necessarily map closed to closed

@sahanar5228

Ай бұрын

Continuity maps Closed inteval to closed interval...but not closed set to closed ..ie ex R

8:17 I have a doubt in selection of option c. We neglect [-1,1] because 0 belongs to it. Similarly option C also have 0. Then why we take as a correct answer?.... Please someone explain me 😢

@DrHarishGarg

2 ай бұрын

The given option is set not interval because 1/n, n€N given .. So we need to find the function corresponding to this set and then check it continuity.... For example, for a and b option, function is given , but for c and d , function is not defined.... That's why, first defined the function and then check... Hope it help you.

@professorragavan9783

2 ай бұрын

Yes sir thank you ❤

🎉❤

😃😃

At 7:50, c is not correct

🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏

❤

Thank you sir😊

Thank you sir

Thanku sir

Thank you sir❤

Thank u sir😊

Thank you sir

Thanku sir

Thanku sir