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Yes that's the one.

Can anyone prove by induction that n(x+a)^(n-1) = sum_{r=0}^{n} r . nCr . x^(r-1) . a^(n-r) for n=1,2,3,... Thanks.

was hoping for a solution. t=tanx and from there. Is that best? Thanks.

I am trying to find the integral of dx/(3+4sin(2x)). Can anyone help? Thanks!

Brilliant. I got to line 4 but did not then multiply by the root x^2-a^2 on itself. Thanks a lot.

Given I_n = integral of x^n divided by sqrt(x^2-a^2) dx show that nI_n - (n-1)a^2I_(n-2)=x^(n-1)sqrt(x^2-a^2). I can't prove it. Can anyone help. Note I_n means I then subscript n like for recurrence integral questions. Thanks!

In what year will the new national Yr 11 and 12 curriculum first be taught to Year 11 students?

Not sure if you guys have seen this before but here is a test that you can use to decide whether or not you are suited to enrolling in Advanced Level Maths at the University of Sydney. Student Self Test It's probably best to take the test after you have completed Integration and Conics from...

Any updates buchanan?

I agree that the method of the proof of irrationality of e that is implied by the latest Ind. trial paper is easier than the methods implied by earlier HSC questions. However, I think that the earlier HSC questions on the irrationality of e (in particular the 1993 HSC question on this topic)...

A good question which is within the grasp of Year 12 students who are keen and committed. It's a pity the exam writers did not require the final limit as n goes to infinity to be taken! T01.

I have had another look at the Calculus Writing Brief this morning and sadly I have found another disappointing feature. This is the removal of "Harder 3 Unit" topics. This topic has created considerable interest in the Extension 2 syllabus and content over the years. Students clearly enjoy...

Comments are based on the material from Buchanan from May 2 under the assumption that those materials will be the basis for the syllabus review. I realise this may not be the case and that further discussion will take place! From a quick look over the Calculus brief it appears that the...

Je ne suis pas d'accord. Moi, j'ai etudie le francais pour HSC il y a longtemps et j'ai utilise la meme methode d'etudes pour tous mes matieres. J'ai recu 95 pour 2U.

The question stipulated that you should use a triple integral and a change of variable - testing the use of Jacobians for triple integral transformations. I agree that V=1/3Ah works for tetrahedra and that 162units^3 is the final result. Also agree with (and am heaps impressed by) the solution...

Find the volume of the pyramid with base in the plane z=-6 and sides formed by the three planes y=0 and y-x=4 and 2x+y+z=4. The question comes from Multivariable Calculus by McCallum et al (1997 version) page 239 Q12. It is at the end of a section on triple integrals and use of substitutions...

for an alternative approach to the problem using internal division of a line, see attached. I have updated the attachment to include all three cases.

I agree Sober - that is simpler for Question One. Of course both ways are valid solutions. Raginsheep - what uni Maths course has those sort of questions? I want the easy credit!

Here is my solution. See attached.

Here is the n=k+1 part of the solution. See attached.