Solved it orally in less than 2 minutes.. I kind of immediately recognised the derivative and then baaki ka bas 20 second ka khel tha.. thank u sir... Yeh sab videos se ek toh approach Krna seekh rha hu sawalon ko and the 2008 que that u took was literally amazing... Bahut kuch sikhne ko milta h.. thanks again sir

Sir can there be an alternate method by just placing x=1,2,3,.... in the function given and from there we can find a relation to solve this

Great explanation for such a difficult question .Great template to follow.

Very good. Question as f(x)->0 can we rewrite as 1/( sinx/f(x)) , now we know lim x->0 sinx /x =1 ,in this case the denominatory is also tending towards 0 ,so we can just make the entire second limit as 1 and we still get 3-1 =2 . (Just checking ,in that case we really dont need the LH rule or even f'(0)? )

Itna easy q in adv wapas nhi aayega

thank u so much sir the level of questions which u discuss is really helpful for advance , plz also try some good problems from standard books

Sir your way of explaining is unique!!!!!

You Are so dedicated sir thank you for this question

Amazing explanation Itna peaceful mind se 0 se hero tak lekr jana is another kind of skill ✨✨👌👌🙏🙏

Sir plz keep bringing good ques like these, they help alot not only for adv but also for mains. Thanks for your efforts❤❤❤

Sir your teaching methods is very good i am preparing tgt math exam it is very useful please give some important concepts

Your teaching method is excellent Sanjeev ji.

Agar is tarah k equation ka root -a huva to +a bhi honga Thereofore is equation k roots even number honge. Clearly x=2 is equation ka root honga. Therefore x=-2 bhi iska root honga Hme rhs me real number chahiye Aur ab x ki koi bhi value is equation ko satisfied nanhi karengi Therefore number of roots are two.

Thanks sir 🙏

Guruji, Pranam!

Nice to see you after a long time sir❤️❤️❤️

Mind blowing solution sir it will help a lot

This is the question of my exam... I still remember 😅😅

very good

very helpful sir. thank you sir

Nice

Superb !!! 🎉

World class explanation. Thanks sir ji.

Sir please take question according to the chapter question and approach

Thanks Sir 🙏🙏🙏🙏🙏

Nice concept and question 👍, Also sir exam is coming near and now I think you covered integration very well now you should start with most asked and important chapters like Vector and 3D , matrices and determinants otherwise it will be too late !!

There is a mistake in the first line of question. Can anybody point out that.

Good explanation sir!!!!!

Beautiful questions,awesome explanation !

4:25 - On the x-axis, 1/2 will be less than 1, isn’t it?

Mind blowing explanation 🔥

Sir please explain sterling number use in PNC

Sir please take a detailed lecture for multinomial theorem

Sir.... please do a graphical discussion of 1/z and 1/z bar in the complex plane

Right now, it is a board-level question

wow …that’s a very clever question!

sir thanks for your efforts

Check MOCK iit 2025 paper by iit professor and students on my channel

thank you sir ji

Final year hogaya IIT mein lskin sir aj bhi old adv ke questions se nostalgia ata hai. Great explanation sir. Aise solve kia apne, great thinking ❤

Sir, your by parts rule is little bit hard to understand, you don't go by exact procedure, first select the function

I tried this thinking in direction of expansion of -ln(1-x) 🥲, anyways brilliant explanation as usual sir

Nice solving ❤🎉

Sir हम t common ले सकते हैं क्या t(log t -1)+c e^x/x(log e^x-logx -1)+c e^x/x(x -log x -1)+c e^x(x-logx -1)/x+c

2(e^u ➖ e ➖ ^u)du

Most clear explanation of this question Hats off to you .

Thanks a lot sir , sir mei phy aur chem ke chakkar mei daily maths manage nhi kar pata kya maths daily karna zaruri hai?

Very well

Thanks Sir 🙏🙏🙏🙏

Sir please solve Trigo Algebra Coordinates Much needed !!!!! 😢