@Sawarnik I'm extremely sorry. I couldn't respond because of electricity failure :( Also upvoted the answer as well. Thanks !

@Sawarnik Yes , I understood it.

Gah, I don't how to respond to little kids! Cute small boys came to be very playfully and I just don't know how to respond!

What?

I have some guests visiting my house. And when tiny playful kids, dunno why they came to me, and they are so very playful with me. But I don't know what to do! I feel very bad.

@AGoogler Ok :))

@Sawarnik I feel exactly the same!

@AGoogler Good! Looks like you are not a very social person?

@Sawarnik Not at all! People call me a nerd.

@AGoogler That is what I meant. I belong to the same category! I am rather too shy actully than unsocial.

@AGoogler What do you think of doing after 12th?

@Sawarnik What most students do , Engineering :( ,

Also I want to give you some bad news

@AGoogler Be different!

WAT?

Oh.

I wasn't selected in the entrance test :(

Rank -128

How much was needed?

40

My net connection is scratchy now.

@AGoogler Oh, you missed it be a long distance.

Looks like there are many intelligent people in Pune.

@Sawarnik Yes.

@Sawarnik There were students from all over maharashtra.

@AGoogler Oh, then it must be tough. But I don't see their business model, why only select 40?

What do you intend to do now?

@Sawarnik Going to Bakliwal tutorials (another class)

@AGoogler Are there any exams for that?

@Sawarnik Yes . I got selected in wizards batch. ( Top 50-60)

@AGoogler Nice! [But I just hate coachings, the time spent there would be better utilized in self-study.]

@Sawarnik Well , that probably wouldn't work with IIT . Further I'm not going to attend college , hence coaching is necessary.

@AGoogler Why is JEE different for that? o.O

@Sawarnik JEE is exam for admission to IITs.

@AGoogler I know of course. But I wanted to know why it is different for coachings?

@AGoogler Besides, I am sorry, but I came to know your name. But don't worry, I forgot it now for all purposes :)

@Sawarnik lol

@AGoogler I hope you are not angry!

@Sawarnik Nope!

@Sawarnik IDK , people say so . It's hard.

@AGoogler Ohk :)

@AGoogler Will you try for SAT?

@Sawarnik Probably not

Y?

@Sawarnik It's costly to go to US for studying , unless you get scholarship

But I heard SAT math is as easy as 10th std math

@AGoogler Trying for the scholarship of course!

@Sawarnik Yep , I'll try

@AGoogler Yup! Just you need to be fast in English.

Yeah

@Sawarnik What about you?

@AGoogler I am a long way from that! So yet to decide. But unless some magic happens, we are bound to get into the JEE queue :((

@Sawarnik Haha!

What did you remove? I didn't see it.

Nothing I was telling that I liked arts too.

@Sawarnik You mean history and stuff?

But looks I wil have to choose PCM :((( :(((

@Sawarnik Start studying physics then ! It's awesome.

@AGoogler When I study it without the pressure of exams, I find arts awesome too. Believe it or not, I have studied half the arts syllabus of 11-12th plus some other books.

@AGoogler Meh.

@Sawarnik WHY?

@AGoogler I don't see why, especially PCM students, discard arts as a bad option. Why, I don't know. Maybe because I like knowing stuff.

@Sawarnik CBSE board?

Yea.

But anyways, nothing compares to maths!

@Sawarnik Well arts subjects in CBSE are good enough. I studied them for NTSE. But maharashtra board is as bad as it gets.

@Sawarnik True , maybe physics is on par too

@AGoogler I am actually surprised the state boards students can be so good. If you are complaining about Maha. Board, I don't think you'll ever find any Bihar Board who can talk in english!

@AGoogler What will you study in maths now? I think we can share our progress.

@Sawarnik Calculus , probability , matrices and determinant

11th-12th std syllabus

@AGoogler Have you studied basic set theory and functions?

@Sawarnik Yes , there was a chapter about sets in 9th std textbook

@AGoogler WAT!

Yes

We are studying irrrational nos for the first time!

And you say set theory!

@Sawarnik Really! Maharashtra board is tougher than CBSE

@AGoogler I think there would have been limits and derivatives in 10th?

@Sawarnik Nope

@Sawarnik But in 11th there is integration , for CBSE it is in 12th

@AGoogler You study the whole calc I in 11th?

@Sawarnik Probably

Wow! Your board is awesome.

But I don't like probability.

And I once tried starting matrices, but found it boring, so it is for a later day.

@Sawarnik NO! They teach harder stuff , but they teach it bad. There are a ton of mistakes in the books.

Oh. You want some calculus questions?

@Sawarnik Sure

@AGoogler Did you try this? chat.stackexchange.com/transcript/message/14660502#14660502

No

Ok, gotta go. Next time I ll give many good ones :)

Then you can try. Want hints?

@Sawarnik Definitely. I've forgot most of calc. I need to learn it again.

@Sabyasachi Good answer for that 30! + 2 ... 30! + 30 question!

@Sawarnik are you there?

@AGoogler Yup!

Just wanted to tell you a good news

@ParthKohli Link?

Now wat!

The result declared was wrong

My real rank is 5!

@AGoogler WAAAAT! Really?

Or joking?

For real!

They called me just now

Ok, in the second correction you will go down again.

But nice! State rank of 5 is wonderful!

Yes!

@Sawarnik NOO!

@AGoogler Oo. Looks like Ajay has got 160!?

@Sawarnik NO idea

Yes

How can it be possible?

Ok, so calculus.

Hint for this goes chat.stackexchange.com/transcript/message/14660502#14660502 divide the interval into equal lengths and apply mvt on each of them.

@ParthKohli Not that great.

@AGoogler You trying?

@Sabyasachi Not that great. But

@Sawarnik what?

@Sawarnik yes

@AGoogler This chat.stackexchange.com/transcript/message/14660502#14660502 with the hint, or should I give fresh questions?

Fresh please

Ok :)

Actually , GTG . Bye :) I'll be back tonight

f is continuous on [a,b].

f(a)-f(a+2)=0

then show there exists a c in [a,b] such that f(c)=f(c-1).

Try this when you come back!