Math OP Level Questions!

My Math Faculty said he’ll be giving 2 Legendary Level Questions Every Day!
I’m Creating this thread to share all the legendary questions!
Please Don’t copy paste solutions for these questions as the fun would go. Try by yourself and discussing with your know sources is most welcome.
Happy Solving !





Bro for first question should we take x^pi + 7 = t ?

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Ya, assuming pie=22/7.
This is too simple, we must be wrong somewhere. !

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Nice point! we usually see pi and e from a high level view and even logarithms and other values are treated as approximations as the aim of the problem is to test calculus concepts. However, what you pointed out is right “Assume pi = 22/7”

How about the second one?


Yeah he said the level will increase slowly xD

I’d definitely try em out.

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Will try again. Got a very bad integral after first sub.
This also gives me a feeling of using by parts after some instant but i am just guessing

Guys is there any Taylor series expansion of

sin(sinx ) ?

Watch this. We can derive it i think but about which number?

Taking Taylor series approx about x=0, I am getting this as the answer:

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Looks correct to me ! Thanks dude

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AH uh i’m a fanboy of 3Blue1Brown

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not getting bro I tried it

See the infinite hotel paradox by Jeff Dekofsky in your free time

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I solved the second question tho. Have 0 clue for the first one. Sir said its a desi INMO Question

Have seen it.

Is the answer the one I posted earlier?

Bruhh. 1st one is one of the toughest IMO problem afaik. Google it.
Lots of youtube videos on it, watxh the numberphile video, i guess is called the legend of problem 6

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