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Was so fun last year, definitely doing this again =)

Here you go.

I only have answers to some selected problems. I will upload in a little bit.

You can typically pick up most marks in conics by knowing how to derive things. If you really can't 'see' how to get the last two marks, who cares - chances are you'll pick up more marks in Q7&8.

Learn to analyse functions!

Looks like it has something to do with polar coordinates.

I'm doing both. Finance/QR plan semi-recommends it.

Iunno dood, the ones I usually see you in xD

Hai Kazi, still lurking UNSW Computer Labs?

That would be likely if it were |e-S_n| < ...

Oh, right. Yeah - (180-2@)/2. Fair call.

Sorry, I thought it was sufficiently clear.

Re: sorry, even more confused now I'm not sure if anybody solved that sin@ = 3@/4 question so here's my solution: l = r@ r = 400/@ Other angles inside triangle are 90-@ Also note that angle at centre = 90 Using simple trig: cos(90-@) = (400/@)/300 = 3@/4 However, cos(90-@) = sin@ ===>...

\text{Let} \,\, I=\int x\sqrt{2x-x^{2}}dx=\int x\sqrt{1-\left ( x-1 \right )^{2}}dx \\\\ \text{Let} \,\, x-1=\sin\theta \Rightarrow dx=\cos\theta d\theta \\\\ \therefore I=\int \left ( 1+\sin\theta \right )\cos\theta d\theta \\\\ \text{Which is easy mode...}

Lul

\text{Let} \,\, f\left ( x \right )=x^{3}-3px^{2}+4q \\\\ f'\left ( x \right )=3x^{2}-6px \\\\ \text{When} \,\, f'\left ( x \right )=0, \,\, 3x^{2}-6px=0\Leftrightarrow x(x-2p)=0 \\\\ \text{Case One}: \,\, f\left ( 0 \right )> 0; \,\, f\left ( 2p \right )<0 \\\\ 8p^{3}-12p^{3} + 4q<0...

y = x^x = e^ln(x^x) = e^(xlnx) dy/dx = (1+lnx)*e^(xlnx) = x^x*(1+lnx) This negates the need to use implicit differentation.

No worries. http://pages.pacificcoast.net/~cazelais/187/maclaurin-sin.pdf should provide some intuition as to where they derived the problem from.

\text{Let} \,\, f\left ( x \right )=\sin x-x+\frac{x^{3}}{3} \\\\ f'\left ( x \right )=\cos x-1+\frac{x^{2}}{2} \\\\ f''\left ( x \right )=x-\sin x \\\\ f'''\left ( x \right )=1-\cos x \\\\ \geq 0 \\\\ f''\left ( 0 \right )=0 \\\\ \therefore x-\sin x\geq 0 \\\\ f'\left ( 0 \right )=0 \\\\...

8 roots there