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Re: MX2 Integration Marathon \int \frac{1}{1-e^{kx}} \ dx

Re: MX2 Integration Marathon \tan x = u^3 \Rightarrow 3\int \frac{u^2\cdot u}{1+u^6} \ du z=u^2 \Rightarrow \frac{3}{2}\int \frac{z}{1+z^3} \ dz (z^3+1) = (z+1)(z^2-z+1) \ \ $etc etc$ Dayum son

Re: HSC 2014 4U Marathon \\ $Consider$ \ \ (1+x)^n = \sum_{k=0}^n \binom{n}{k} x^k \\ \\ Re(1+i)^n = \left(\binom{n}{0} + \binom{n}{4} + \binom{n}{8} \right) - \left(\binom{n}{2} + \binom{n}{6} + \dots \right) \ \ \ \ (1) \\ \\ $Also consider that since$ \ \binom{n}{0} + \binom{n}{2} + \dots =...

Re: MX2 Integration Marathon \\ \int \frac{1-t^2}{t^4+8t^2+1} \ dt

Re: HSC 2014 4U Marathon Seeking to transform this equation into a reducible quadratic, we substitute, x=t+q (t+q)^4 -32(t+q)^3 +387(t+q)^2 - 2096(t+q) + 4290 Now, we find the value q such that the co-efficient of t^3 and t are zero, by equating co-efficients, we find that if we let q=8...

Re: HSC 2014 4U Marathon Yep thanks for the correction.

Re: HSC 2014 4U Marathon \\ $Using complex numbers, prove that if on a quadrilateral, two sides are opposite, equal and parallel, then the other two sides are parallel and equal.$

Re: MX2 Integration Marathon u=-x \Rightarrow \int_{-a}^a \frac{f(x)}{1+e^{x}} \ dx = \int_{-a}^a \frac{f(-x)}{1+e^{-x}} \ dx \frac{1}{1+e^{-x}} = \frac{1+e^{x} - 1}{1+e^{x}} = 1 - \frac{1}{1+e^{x}} \therefore \int_{-a}^a \frac{f(x)}{1+e^{-x} } \ dx = \int_{-a}^a f(-x) -...

Aha I'm alright I guess, what about you? Well what's happening right now is that I have to pick between BEng and BSc (Adv Maths) very soon and I'm leaning towards BEng.

Hmm ok I see, if I can transfer credit over for the maths courses, would I still need to do some other science units? (I'd already do some in my BEng first year) I need to know whether I can or not because I'm pretty much 50/50 split between a BEng and BSc Adv Maths course and if I can just do...

According to: http://sydney.edu.au/science/cstudent/ug/forms/transfer.shtml If I do a BEng in USYD, while doing the appropriate Adv Maths units (MATH1901 and etc), will I be able to internally transfer to 2nd year BSc (Adv Maths). Or would I need to start it again? Thank you

Re: HSC 2014 4U Marathon A (2 dimensional) ball with radius 'r' has a fixed red marker on it. It is rolled along the flat ground and the red marker leaves a trail in the air. If the ball was initially above the origin with the marker being at the origin. Find the Cartesian equation describing...

Re: HSC 2014 4U Marathon $Prove for positive integers$ \ n \\ \\ \sqrt[n]{n!} \leq \sqrt[n+1]{(n+1)!} In case latex is down it is asking to prove: (n!)^(1/n) <= ((n+1)!)^(1/(n+1)) for positive integral n

Re: HSC 2014 4U Marathon Just checking, but is the answer p=2?

Ah well lol

Alright, here we go: First we establish that our flips can be expressed in a string of Hs and Ts representing Heads and Tails respectively. The structure of this string will have to be: _ _ _ _ _ ...... _ T H H H H .... H Note, that is an 'n' number of Hs in the end of this string, we need a...

How does one even calculate an average? Is it: \sum_{m=1}^{\infty}mp_m p_m being the probability of getting n heads in a row in m throws.

Not God of the gaps, according to what is known I am drawing the conclusion of design, not according to what is unknown. It is not 'I can't explain the origin of the cell, therefore God', it is, 'the cell bears likeness to design just as our factories and software programs bare likeness to...

Re: HSC 2014 4U Marathon \\ $If$ \ \alpha , \beta \ $are roots of the equation$ \ x^2 + px + 1=0 \ \\ \\ $and$ \ \gamma , \delta \ $are roots of the equation$ \ x^2+qx+1=0 \\ \\ $Prove that$ \\ \\ (\alpha - \gamma)(\beta - \gamma)(\alpha + \delta)(\beta + \delta) = q^2-p^2

Re: HSC 2014 4U Marathon \\ $Find$ \ b \ $if the equation$ \ \ \ x^4 + ax^3 + bx^2 + cx + d = 0 \ \ \ $has rational coefficients and 4 complex roots, two with sum 3 + 4i and the other two with product 13 + i.$