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Next Question If y = (√[1 - x2])·sin-1x, find dy/dx. Express (1 - dy/dx)·(x-1 - x) in terms of y.

Consider the binomial expansion of 2^n = (1+1)^n whilst acknowldgeing this relationship: nCn = nC0 nC(n-1) = nC1 nC(n-2) = nC2 etc... If n is odd: (1+1)^n = nC0 + nC1 + nC2 + nC3 + ... + nC(n-1) + nCn (1+1)^n = nCn + nC1 + nC(n-2) + nC3 + ... + nC1 + nCn (1+1)^n = 2(nC1 + nC3 + ...

Yes, I just entered that into mathematica and got this: I would not argue with that, the question does seem quite unconventional mixing polynomials with trig, where did you find this question?

That does not apply here, did you not read any of this thread? An example, how many whole integers are in 7.9? The answer is 7. Often you have to look at the context.

Surely i) is actually: As for ii):

Your first term is correct but the second term should be -li(x) where li is the logarithmic integral which is beyond the scope of the 4u course.

Edit: pluvia and I keep posting at the same time, anyway here is an alternative way of solving it We have a curve and a line, if we simultaneously solve the two equations for x, then there should be exactly one solution since they intersect at only one point: y = kx2 y = 8x-4 kx2 =...

Latus rectum is a line that is parallel to the directorix and passes through the focus. I don't know what is meant by "four standard forms", but with the given information I can tell you that the focus is (0,1) so the porabola is x2 = 4y

0/0 is an indeterminate value meaning that it cannot be solved, its value could equal anything on the number line. So although the two answers are different they are not conflicting.

I found the answer sheet to this exam (MX2 CSSA 2005) amongst my notes and have uploaded it to a server, PM me for the URL.

P(x) = (x-a)2 * Q(x) P'(x) = 2(a-x) * Q(x) + (x-a)2 * Q'(x) = (x-a) * (2Q(x) + (x-a)Q'(x)) = (x-a) * R(x)

A mathematician, a programmer and a statistician are hunting deer. The mathematician takes the first shot but aims too high, the programmer takes the second shot but hits the ground sever feet before it, and at this moment the statistician jumps up yells: "We Got Him"! Also quite funny: How...

I found it to be quite straight forward. Only one multiple choice question didn't make sense and the short responses were not obscure at all.

If you use calculus and make an error there is a much greater chance you will lose marks than if you had used the simple formulas provided and made an error. If you are smart enough to understand 3 unit maths then why must you find these simple formulas hard? They are essentially the same...

A number that is the solution of a quadratic equation with integer coefficients. That is a number like (3+√7)/5, you should be able to perform addition, mutliplication, division and subtraction of them as well as being able to rationalise the denominator if necessary.

A short moment of rejoice as I get drunk and forget my curses. Then its straight into making those dot point summaries I should have done all year.

If you find that you cannot solve a problem like that with a limit then most of the time you can just sub 0.0001 into the calculator as x then key in the expression. Most of the time it will give you an answer considerably close to the correct one such as 0.9997. The only times this does not...

I found some parts to be quite challenging, the only part that I had no idea with though was the last part of question 7. As others have said, do not post the questions, I have competitors who have yet to sit it and they may be reading.

I am not sure how this would be solved without a computer but this is the result I get using Mathematica: N[(Pi^-199.1351208912179) - (E^-227.9559242064109)] = 5.55911x10-112 Being positive suggests that the Pi expression is greater.

It is a little stickier than undefined it is indeterminate. This means it may have a value in some contexts with more information.