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Thanks guys. How'd you do this one? I'm guessing it's really simple comparison like the one I posted above, just can think of the proper one...

Thanks IG, leehuan and Paradoxica: leehuan, how'd you get rid of the equality in this one?: Also, is this correct?

Thanks for that, I'll figure (3) out now too... Got another one, from series this time, I'm completely stuck: Also, is this correct?

Thanks! I've got a few more... EDIT: Figured out two, I've deleted those from here

These as well, please, if anyone could solve these that would be great. I'll be posting more questions up as exams are roughly in a month... \\\text{(1) Two examples involving time explicitly: }\\\text{(a) Seasonal variation: Solve }\\ \frac{\mathrm{d} y}{\mathrm{d} t}=k(1+\text{a} \cos(2\pi...

Got more questions...pls help: \\\text{(1) Solve }2y'y'' = 1 + (y')^2 \text{ by letting }y' = v\\\text{(2) Use the substitution }v= \frac{\mathrm{d}y }{\mathrm{d} t} \text{ to solve } \frac{\mathrm{d}^2y }{\mathrm{d} t^2}+\omega ^2x=0\text{. Here obtain a differential equation in }v\text{ and...

Always think of fat clients as clients that can do processing of their own, i.e. they have a CPU. Examples include your home computer (it can process and display it's own data with software installed on the machine, it doesn't need anything else to display information). On the other hand, thin...

Sorry for the late reply, figured that one out, thanks :D

For this question: \\\text{Let }f(x)=\sqrt{1+x}\text{ and suppose that }a_1=3\text{ and }a_{n+1}=f(a_n),\forall n\geq 1\\\text{(a) Prove that }a_n^2-a_n-1>0\forall n\geq 1 What would be the best approach to do this?

Yeah I've noticed that too, but what surprised me the most was that some of these assumptions seep into the actual HSC exam too. This is why in HSC, students that may be aware of such facts may find it logically challenging to solve problems by riding on such assumptions, where they fail to draw...

Thanks again, but yeah reading about the Golden Ratio, it is quite unique.... Anyway, finally get the general approach for such questions, thanks to the process just posted (I guess I was kinda overwhelmed by the trivial roots inside the roots thing that they gave at the end. I know it's an...

Thanks so much! Btw, how'd you know the limit in (e) was the Golden Ratio? Is it just a property of the ratio, or is there a rule/theorem attached to this?

For practicals, you have to make sure that you have your theory linked to its practical applications. They would've told you at least what topic the exam would be from, so make sure that you're able to justify all the chemical reactions in that section/chapter with ease, i.e. linking any...

Thanks! Just a few queries: (b) can we directly state that 1\leq a_n \leq 2 for all n, even though there is a condition in (a) that x has to be between 1 and 2 (inclusive) (c) I get the logic, but is that all I need to write for c? if not, what do I need to prove? (d) What is the Monotone...

I had another question: \\\text{The limit of a recursively defined sequence.}\\\text{Suppose that }a_1=1 \text{ and } a_{n+1}=\sqrt{1+a_n}\text{ whenever }n\geq1\\\text{a) Show that }\sqrt{1+x}\in [1,2]\text{ whenever }x\in [1,2]\\\text{b) Use induction to show that the sequence }\{a_n\}\text{...

Thanks

No he didn't :( Wait, how'd you do the implicit diff part?

Hey everyone, I've got another question: \\\text{Solve }x^2y''-2xy'+2y=0\text{ by:}\\\text{a) letting }x=e^t\\\text{b) letting }y=x^m

Is it true that: \text{If }X_1 \sim \text{Pois}(\lambda_1), X_2 \sim \text{Pois}(\lambda_2)\text{ then }(X_1+X_2=n)\sim\text{Pois}(\lambda_1+ \lambda_2) If so, what theorem is it?

Yep, thanks :)