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Does anyone know the complete proof for a curve to form a loop, for example if you are to prove that this curve:x=t^2 and y=t(4-t^2) forms a loop??? THanks in advance, guys

is it worth going?

Actually I didn't forget anything. In my country the schedule is kind of the same throughout the whole year. @@. What worries me is that the entry exams to Universities gets harder and harder each every year :spzz:

my teacher said we can have tan (pi/2) = infinity (or "undefined" but "infinity" is preferred in this circumstance") and the result was pi/3

I can't see the graph @@

arrrrgh

I wonder when it would go to the point where everyone goes tutoring, like what happens in some Asian countries where people have to kind of go to two 'schools' at a time, one is their 'official' school in the morning and the other is the tutoring college in the evening. LOL

hu hu hu that is NOT fair

Thanks for your explanation. btw how did you get to know all these things such as the "improper integrals"?

Even if the integral seems to approach (pi/3) when x approaches pi as you've stated above, pi/3 still can't be regarded as an answer can it? In fact I find it hard to accept that tan (pi/2) really exists and can be used during the calculations.

Where did you get these figures from? Btw In class my teacher 'solved' this question by making a table of values. She has always been so unreliable...

The domain, or x should be from -1 to 1. btw the answer in the text book (the range) is from (-pi) to less than (pi/2).

How would you find the range of y= xcos^-1 x ??

If n=0 isn't it true that U (n) becomes U (0) = S 1/ (5-4cosx) dx [ from x =0 to x= pi] ?

Yea, true. Thanks

No. that was the full question. btw can you explain a bit more, what does " n=/=0" mean?

Alright that was what happened to me = =! I think the only possible explanation is that the question itself is wrong! Is there anyone who has done or seen this question before???

I'm not used to Latex so I only wrote my working on papers... Anyway, if the (2/5) from the third or fourth line is supposed to be 'there' then your method will not lead to the answer pi/3 How come you Study-freak and Drongoski both arrived at the same answer? @@

I don't think it's a typing mistake though @@

Can we really write like this in the exams?