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everything that has been posted here is irrelevant the aspect of chess that makes it sport-like is the fandom and the audience/culture that is created around the elite players commentators, supporters, etc. just like any other e-sport

don't try it's hopeless :biggrin: on the other hand you never know unless you shoot your shot

Here is a decidedly slicker way to decide which root is α (IMO) in this image, α = t

Consider the trigonometric form of α-β by rewriting it in terms of powers of ρ

the real answer to this conundrum is that by using a substitution which maps a finite open interval to ℝ, you cannot invert the substitution to obtain an antiderivative valid over all of ℝ. the substitution is only bijective locally, not globally, so a true inverse does not exist, hence the...

Define \psi(a,k,u,v) := \log_a\left(a^{u} + k + a^{v}\right) The original question takes the argument a=2. For brevity, we will suppress the first two arguments⁰, as it turns out they are irrelevant to the final answer. (This is a thing in higher mathematics lmao get used to it) The...

Not everyone has such generous life opportunities though. Some of us grew up just trying to survive in a hostile home AND school environment, parents who don't care or understand, an unreconcilable communication barrier with parents, and a plethora of neuro/psych impairments. Mathematics was my...

*looks at the world* you're out of your mind

So I solved (v) with two applications of the Stolz–Cesàro theorem, I have given up on attempting a more within-the-syllabus proof.

I'd like to speak to the author of this question grabs knuckle dusters

i'll put the dox in paradox for $100 ;) i won't pls don't harass me to reveal the name

numbers have an end therefore all decimal expansions terminate therefore all real numbers are rational ⬛ this is satire btw

personally, 16 (a) is the harder question for me, because i understand irrationality proofs like physicists understand newtonian mechanics

Remark: For the Induction in MX2 13 c i, many students tried to differentiate the recurrence and arrive at the given definition of the Hₙ(x) Polynomials. While this was not an invalid way of doing the problem, it made your life 100 times harder, as manipulating so many expressions at once was...

could also scan it not sure how much easier that would be e: on second thought it's not terribly inconvenient to meet up at parramatta to arrange it

Not an HSC student but you should go have an existential crisis for the next 3 years.

tried this as my initial thought (i knew getting rid of the denominator was a necessary step), didn't get very far for some reason, maybe i made an arithmetical error somewhere

I can reduce it but I can't evaluate it. Are you sure this integral is expressible in terms of elementary functions? The numerical integration returns 0.4690815321272337326612091235046416327076, which has no simple form in the Inverse Symbolic Calculator.

This is completely valid but technically requires induction to complete the argument for all naturals.

whodis y u follow me