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This was from the sample from nesa. Part i asked prove that a *(b+c)=a*b+a*c (dot product)

Ive seen this on AceHSC or something

Oops ahaha thanks. Forgot about that, but they are both a difference of some sort. Sorry

You mean differentiate both sides? Cause derive is completely different. If thats what you mean, then yes, I also said that I did use differentiation initially to obtain the result... my comment was simply that mathematical induction is still valid. When I looked at the question a second time...

The limitting sum is a/(1-r) and the sum to n terms is a(1-r^n)/(1-r), where r is the common difference. The common difference for a gp is achieved by dividing nth term by n-1 term, and if this quotient is consistent for more than one pair of terms, then the series is gp. The way in which the...

Yeah, I just found my older solutions to the paper and thats what I did. Again i just used that as an example. Theres nothing wrong with induction though in the case where you dont immediately recognise something.

Its not GS the way its given to you. 3x/2 is not 4x/3, so there is no common difference unless you re arrange it. In the case where youre not bothered like me, induction should be fine. Sorry I used the term convergence a bit too broadly, what I meant is proving that it equals something, i.e...

You then would use the horizontal displacement formula x =vcos(alpha),apply the same process except with this formula. Minimum achieved by simple trig by referring to the building as a side of a right triangle, the base 20 and height 13 (15-2). Tan alpha = 13/20 so alpha = 33 is a minimum...

Yes I corrected myself earlier. Have you seen the method to use if you were to take this approach that I described?

Yes I would know how to prove both of them without the use of induction as it isnt necessary for any of them. Suppose a statement were set up and you can identify two variables, one that would act as x and another as n, then prove for the valid set of n by induction. Proving that a series...

The question showed up in a BOS trial exam for 4 unit - I don't remember it that clearly but it was about proving 1 + 2x +3x^2 .... + nx^(n-1) = some expression in terms of x and n. My instinct was to use induction as it was a sequence, and proving that it converged to a certain function would...

Hey everyone, I wanted to ask whether or not you can use induction to prove something even if the question does not ask to use induction. Would you lose marks? Thanks

Hope this helps. Correct me if im wrong (see attachment), I dont know if there are solutions to the paper

I found the mistake!!! Where i evaluated the integral containing (ipi + lnx)^2, i forgot to reconsider the second integral, I2, after proving I1 =-pi^3/2, which happened to be I. Therefore you are left with ipi^3/2 + 2I = -pi^3/4, and I = pi^3/8.

I honestly dont, but pi^3/8 is the value you got from wolfram yesterday, so definitely a mistake. But where......

I have attached a copy of my solution. Turns out i didnt get 0 this time, but got pi^3/4... do you see mistakes? Thanks

Oh thats fine. I hope one day to take analysis after school. Not real analysis, never really into it, but i like complex and functional

Yes I see it now. I did split ln (-z) to ipi + lnz, and used it wherever it needed to be. That was the reason i kept getting 0

The question is meant to be loge x squared. ive seen that and applied the same thing but get 0... ill send my answers tomorrow

I cant see your latex text