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Re: MX2 2015 Integration Marathon \\ $i) Show that$ \ \int_0^{a} f(x) \ dx = \int_0^a f(a-x) \ dx \\ $ii) Hence find$ \ \int_0^{\pi /2} \frac{\cos^{4}x}{\sin^4x + \cos^4x} \ dx

So I was thinking of whether the following inductive statements are logically valid: Say we have 2 statements, S_1 and S_2 \\ $For the base case,$ \ S_1 \ $is true, assuming$ \ S_1 \ $is true for the general case, then if$ \ S_2 \ $is true, then the inductive step for$ \ S_1 \ $is true$ \\...

Man all the poems on this thread are terrible except for mine

WORK -------------------------- They told me to work for a school __So I worked for a school They told me to work for a job __So I worked for a job They told me to work for money __So I worked for money They told me to work for a home __So I worked for a home They told me to work for a family...

How do you guys warmup for a competitive match (if at all)?

I just got MGE earlier today :^D May or may not be short lived

Re: MX2 2015 Integration Marathon \int_0^{\pi /2} \frac{1}{1 + \tan^4 x} \ $d$x

Re: MX2 2015 Integration Marathon Another method: \frac{1}{1+e^x}= 1 - \frac{e^x}{1+e^x}

Re: HSC 2015 4U Marathon - Advanced Level \\ $Let$ \ a_0 > 0 \ $and$ \ a_{n+1} = a_n + \frac{1}{\sqrt[k]{a_n}} \\ \\ $Show that$ \ a_n \ $does not converge as$ \ n \ $increases without bound$ ----------------------- \\ $HINT: Consider$ \ \lim_{ n\to \infty} (a_{n+1} - a_n) \ $. Then make an...

Re: MX2 2015 Integration Marathon \\ \int_0^1 \frac{dx}{1+e^x}

Re: MX2 2015 Integration Marathon You have to solve my integral first, one question at a time

Here post integrals for helping 2015 students with integration! Do not post a question until the last one is answered Do not post in the other thread because that is locked ------------- \int_0^{\pi /6} \sin^4 x \cos^3 x \ dx

Re: HSC 2015 4U Marathon \\ $If$ \ p(x) = x^3 + px + r = 0 \ $has root multiplicity of 2, then$ \ p'(x) \ $has a root in common with$ \ p(x) \\ \\ p'(x) = 3x^2 + p = 0 \Rightarrow \ x = \pm \sqrt{\frac{-p}{3}} \\ \\ $If$ \ x = \sqrt{\frac{-p}{3}} \ $is a root, then$ \ p\left(...

Re: HSC 2015 4U Marathon \\ $If$ \ \alpha, \beta, \gamma \ $are an equilateral triangle, then$ \\ \\ (\beta - \alpha) (cis \frac{\pi}{3}) = (\gamma - \alpha) \\ \\ (\gamma - \beta) (cis \frac{\pi}{3}) = (\alpha - \beta) \\ \\ (\alpha - \gamma) (cis \frac{\pi}{3}) = (\beta - \gamma) \\ $So,$ \...

What rank are you?

I'm MG2 I only play Dust2 and Nuke (yes I'm a noob) (sometimes Inferno) I have a similar username on Steam to here so you might end up versing me (if you haven't already)

Re: HSC 2014 4U Marathon - Advanced Level 1 + x + x^2 + \dots + x^{n-1} = \frac{1-x^n}{1-x} x + 2x^2 + 3x^3 + \dots + (n-1)x^{n-1} = x \cdot \frac{d}{dx} \left(\frac{1-x^n}{1-x} \right) \sum_{n=3}^{\infty} \frac{n}{2^n} = \lim_{n \to \infty} \left(x \cdot \frac{d}{dx}...

Re: HSC 2014 4U Marathon - Advanced Level _____________________________________________ NEW YEAR 2015 ______________________________________________c

Yeah but I didn't say the latter so I didn't make that statement

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