Yes , the answer is 2.

Consider the graph of that f(x) = [x] for the interval 2<x>3.

See , as we move towards the point x = 5/2 , the graph on either side of that point is a straight line , with a constant value i.e. 2.

So, the limit exists.

If the question would have been like find lim x -> 2 [x] , then your argument holds.

K.C. Shinha - Solve the whole book.

Use Thomas and Finney only to clarify the difficult parts.

Don't keep a target of studying x number of hours.

Keep targets of completing something , say , some problems for that day.

As far as planning is concerned , plan your day the moment you get up from bed.

My advice is try to keep pace with the class.

Also , I would say, utilise minute and minute to study (Of course , take exerices and relax for 5 min. after every hour of study).

Yes , probably, the exam pattern will chage this time. I also expect the "eligibility" criteria to become tougher.

But , don't worry, even if the pattern changes, it will have the same effect on everyone.

Wish Granted. But , you will not be able to discuss anything with them. You will talk only of GIRLS!!

My Wish : I want a super - brain like Einstein. So , study less and enjoy more!

And coming to pattern , the JEE people can change the pattern for JEE 2009. There is no rule which denies them the chance , even to change the "eligibility" criteria.

The official JEE Declaration is made in October - November. So , we will have to wait.

No! Yaar , admissions in IIT will never be made on Board marks. This is due to the fact that there are 25 boards in India , whose examinations vary in a great deal :

1. Level of difficulty

2. Portion for it.

The IIT people will of course want their students to have some basic skills and a basic knowledge to maintain their standard. So , if you ask me JEE won't be scrapped.

However , I anticipate a change in the pattern of JEE. It may become somewhat subjective. A mix of obj + Sub. if you ask me. Quality questions without giving answers!

I also feel that these people may keep some sort of "interview" of the JEE qualified students to finally screen the one's they want. Like , the NDA interview or IIM admission! This seems to me a perfect solution , the profs can then and there select or reject whoever they want. As far as "screening" and "mains" are concerned , I think it's won't be re-introduced. If introduced , it will again introduce the problem of repeaters (For the very reason , it was scrapped).

Coming to coaching classes , interviews seem to me the best solution. I also , feel that the "eligibility" criteria of JEE will become tougher (like 75 % agg. marks in 12th) or so ; to pull the attention of students to Boards.

I'm sorry. sinx/x is integrable , but it's integral cannot be found by conventional means.

See , when you integrate f(x)dx you must make a substitution that fits in the domain of f(x). For example , if you are integrating 1 / sq. rt ( 1 - x^2). You must make a substitution that sees to it , that it does not attain negative value. Consequently , you cannot substitue x as tanx or secx etc. However , you substitute x as sinx or cosx.

Similarly , while integrating F(x) = x^xlnex dx , we make the substitution x^x as k and then take log and then differentiate , thus concluding that it is defined for only positive values of x.

F(x) = sinx/x is a discontinous function at places where sinx = 0. Thus we must make a substitution or transformation that makes it clear that the function will only attain non - zero values , between the domain ( 0 , pi) , (pi , 2 pi) and so on.

However , it is impossible to find out such a substitution or transformation.

Hence , f(x) = sinx/x is not integrable by conventional means.

As a trivial method , expand sinx  , divide by x and then integrate , the infinite series. At least , you will get an approximate value of the integral.

six/x is not integrable because it is discontinous. Remember that sinx is a periodic function and attains 0 value.

Arre , first note that it is only self-study which is going to land you up in IIT. Coaching classes only give you a direction and keep you on your path.

Your question should have been "Can I qualify IIT JEE with no coaching class"

Well , you must know that for clearing any entrance exam 90 % of the contribution comes from the self and the rest 10 % from guidance. However , how this 90 % of time or say hard work is gonna be spent entirely depends of the rest 10 %.

So , my opinion is that , coaching is necessary. In case , you can't afford , you must get hold of a person who will tell you what to do and what not for the JEE i.e. which books to follow and how to plan your time.

Coaching also helps you in one way. You get infact more time to study as your doubts are cleared by your professors. In ablesense of it ,you will have to do your own research and ask your friends - both of which cannot be trusted.

Yes , the function must be continuous everywhere in the domain of integration. Otherwise break the integral. The best example of this is integration of [x] function (Greatest integer function).  To be frank , all functions are integrable. The only hitch is that we do not know the methods of integrating it.

Generally , if a smooth graph of the function exisits , it is integrable. You must have heard formulas that are avalable for evaluating definite integrals. They can be applied for any function provided is continous and differentiable in the domain of integration.

If you want to find out indefinite integral of , say f(x) = x / logx , you can pick up any of the formula for evaluating definite integrals. Put the upper limit of integration as "x" and the lower limit of integration as 0. This is beacuse f(0) = 0. Thus you will get the indefinite integral. However , please note that it will not be accurate. As you know , most of these formulas , ask us to break the domain into parts. So , you must evaluate the limit as the number of parts become infinite. By using this method , you will be able to integrate any integrable functions.

Notice , that this is the very basic idea of "integration defined as the summation of terms".

Formulas that you can use : Trapezoidal rule , simpson's 1/3 rule etc.

However , if you want to find whether a function is integrable or not then you must :

1. Check whether the function is continous , differentiable and well-defined (it does not attain abusrd values) in the domain of integration.

If this condition is fulfilled , then the function is integrable , else not.

This again comes from the very basics of integration which relate it to summation of infinite terms.

Cheers,

Yes , you can still do it.

All you require is structured planning + Planned Hard Work + Smart Work .

All your work must be smart work.

Smart work means solving quality questions.

Some tips :

1. Gradually increase the level of questions you solve.

2. Solve each and every question in specified time. Don't look into the solutions impatiently. Learn the basics concepts the problem demands.

3. Solve good , quality problems.

4. Pay more attention to topics that are frequently asked in the JEE.

5. Write as many mock tests as many possible. Analyse your mistakes from them and rectify them.

6. Do not neglect your board exams. Study for them seriously. Write mock tests and get evaluated from your teachers

7. Consult your sir and discuss your problems in detail with him.

@ praps2510 (5)

IIT Roorkee lies in the state of Himachal Pradesh.

Yes, it is true that one state cannot have two IIT's. UP has two institutes of technology which accept JEE qualified students due to it's large size.

The reason is "quality of opportunities" for all states and proximity of IIT for all state aspirants.

I have also heard that IT-BHU is gonna be IIT next year. It can be , but it cannot be said for sure.

Cheers

Yea , I gave SAT.

No!

But I am financially very strong.

But my problem is that I want to repeat IIT , but my dad is against it. He says there I will get good exposure (international crowd) and all + the best education.

He is against me repeating.

Does anyone know of this university? If yes , tell me something.

No! I don't think that IIT standards would be compromised. In fact , what I feel it will improve. Why? So little seats , so much competition! People will surely study with greater efforts. Even OBC's will - coz in the gen. category they know they can't stand a chance with minimum efforts and even they have competition in their listings.

BITS is what I personally dislike. Why? It's a personal reason. I couldn't go bcoz of the damm 8- % thinng . Got 79.86 % in PCM.

But still BITS quality is improving. Not because of their efforts , but increasing number of because students are becoming aware about these things and have started to work hard.

But , whether BITS will overtake IIT can't be said. It's for us to wait and watch. In industries , where most of you are gonna work , analytical abilities and maths plays no role. All it takes is some street-smartness and courage.

Come what may , IIT's will surely find ways to screen the students they want - the JEE!

It's not under govt. control.

So , study hard!

My Scores :

IIT - AIR 5000

AIEEE - AIR 7616

BITSAT - 345

Hi!

I am getting admission to University department (Information Technology) of Pennyslavania state university for BS (Equivalent to B-Tech)

Should I go? Does anyone know about this university?

How is it?

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