Re: HSC 2016 4U Marathon - Advanced Level
Yes this is what I got as well, I wasn't able to find a closed form either which is why I simply asked for an expression
Some exercises in formal logic:
\\ $Prove formally the following:$
\\ $1.$ \ p \Rightarrow (q \wedge r) \vdash (p \Rightarrow q) \wedge (p \Rightarrow r)
\\ $2.$ \ \sim p \Rightarrow p \vdash p
\\ $3.$ \ (p \vee q) \Leftrightarrow p \vdash q \Rightarrow p
For a list of the symbols used...
Re: MX2 2016 Integration Marathon
Yes well done, alternatively x= \tan u and then v = \frac{\pi}{2} - u , adding up the integrals in u and v to get what you have.
Re: HSC 2016 4U Marathon - Advanced Level
\\ x \ $is a real number randomly chosen from the interval$ \ 0 < x < 1
\\ $Let$ \ f(x) = \left\{\frac{1}{x} \right\} \ $where$ \ \{A\} \ $is the fractional part of$ \ A. \\ $Examples of this function include,$ \ \{\pi \} = \pi - 3 \ $or$ \ \{1.5 \}...
Re: HSC 2016 4U Marathon
\\ $By the very definition of differentiability$ \ f \ $is differentiable at$ \ a \ $if and only if the limit$ \ \lim_{h \to 0} \frac{f(a+h) - f(a)}{h} \ $exists$
\\ f'(a) \ $is also simply the name we give to this limit, and since$ \ f'(a) \ $is independent of$ \ h...