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Re: HSC 2013 3U Marathon Thread damnn i never knew until now...lol

Re: HSC 2013 3U Marathon Thread \small A^{n+1} - A^nB + B^{n+1} - B^nA = (A-B)(A^n - B^n)\geq 0 \\($because \dots if A $>B,\therefore A-B>0, \therefore A^n-B^n >0, \therefore (A-B)(A^n - B^n)>),$ same thing happens when A$<B$) \\ $ $ And equality occurs when A = B$ \\ \\ $If ($A-B)(A^n-B^n)...

Re: HSC 2013 3U Marathon Thread $\underline{Consider} $ y = x^x = e^{xlnx} \\ \frac{dy}{dx} = x^x(lnx+1) \\ $For \underline{stationary} points, $\frac{dy}{dx} = 0, \\ x^x \neq 0 \\ lnx+1 = 0, x = \frac{1}{e} , y = \left ( \frac{1}{e} \right )^{\frac{1}{e}} \\ $Sign of $\frac{dy}{dx} = lnx+1...

Re: MX2 Integration Marathon $Find $\int \frac{dx}{(1+\sqrt{x})\sqrt{x-x^2}}

Re: HSC 2013 4U Marathon oh right thanks!

[1] - look above [2] - solubility rules are to be committed to memory if u want - its quite beneficial (it wont be provided in any test) [3] - yes its good to - such as confirmation tests (eg. after adding nitric acid to unknown sol'n, if fizzing occurs, carbonate ions are present, THEN we...

All ions listed in some other dot pt: perform first-hand investigations to carry out a range of tests, including flame tests, to identify the following ions: - phosphate - sulfate - carbonate - chloride - barium - calcium - lead - copper - iron

do u go JRHS or are u asking for ur friend(s)?

yep this is a more superior explanation than mine would my answer receive full marks? or must i also explain that in this time domain, the particle goes in ONE direction (doesnt change direction and doesnt stop)?

(I) From this, apply tangent ratio tan\theta = \frac{h}{100} The rest if ur job to do (II) $R.T.S $\frac{d\theta}{dt} ($when h = 2000) \approx $\frac{11}{8020} Simply apply chain rule \frac{d\theta}{dt} = \frac{d\theta}{dh} . \frac{dh}{dt} Note: \frac{dh}{dt} = -55 -ve because he is...

Doing (d) (e) (ii) \dot{x} = \ tant \\ $$\frac{dx}{dt} = tan t \\ dx = tant \ dt \\ \\ x = \int_0^{\frac{\pi}{3}} tant \ dt Apply simpsons rule (look back in ur notes/textbook/internet to obtain the formula) This means we find the distance TRAVELED from initial time (t = 0) to desired time...

Re: HSC 2013 4U Marathon nvm i thought pi and e on the calculator were exact...

First one: P(c) = c^2 ...(1) Second one: P(d) = d^2 ... (2) P(x) = (x-c)(x-d)Q(x) + px + q (remainder has a degree less than of the divisor - it can be a consant or linear) Apply ..(1) P(c) = 0 + pc + q = c^2 pc + q = c^2 ..(3) Apply ..(2) P(d) = 0 + pd + q = d^2 pd + q = d^2 ..(4)...

Where is 4 and 5b?

damnn woops lol

In ur 2nd method Carrot, A can be (2-i) because of the fantastic complex conjugate root theorem! Since (2+i) is a complex root, then its complex conjugate (2-i) is also a root

haha

Product rules is used when u have a product of 2 functions eg. xe^x Here is a very good question: Given that y = (x)(x^2 ) Using product rule or otherwise, find dy/dx

There is no problem with 4x I wanted to show u that u made a multiplication error while differentiating this particular term so i neglected the 4x unless ur talking about Asianese's working, he just used product rule I dont clearly see ur problem with this....

Asianese perfectly differentiated it, maybe u did a multiplication error y = (3x-2)^5 dy/dx = 5 . 3 (3x-2)^4 dy/dx = 15(3x - 2)^4