Search results

Prove the following statement using mathematical induction 7+77+777+...+77...77=\frac{7}{81}(10^{n+1}-9n-10)\quad\quad\text{where}\quad n\in\mathbb{Z},n\geq2 The last term on the L.H.S has n-digits

Re: HSC 2017 MX2 Integration Marathon stuck on this one, any ideas? \int \frac{(2+x)e^{-x}}{x^{3}}\text{d}x

Re: HSC 2017 MX2 Integration Marathon By the 'remember the answer' method we have \frac{\pi\sqrt{2}}{4}

Re: HSC 2017 MX2 Integration Marathon Using the fact that \int_{-\infty}^{\infty} e^{-x^{2}} \text{d}x=\sqrt{\pi}, Evaluate \int_{-\infty}^{\infty} 3x^{2}(x^{3}+1)^{2}e^{-x^{6}-2x^{3}} \text{d}x

Re: HSC 2017 MX2 Integration Marathon Using a hyperbolic trigonometric substitution, show that: \int_{0}^{1} \frac{1}{1+x^{4}}dx=\frac{\pi+2\ln(1+\sqrt{2})}{4 \sqrt{2}}

Re: HSC 2017 MX2 Integration Marathon \frac{n\pi^{2}}{2}

Re: HSC 2017 MX2 Integration Marathon $Let$\quadI=\int_{0}^{\pi} \frac{x}{\varphi - \cos^2{x}} dx By the reflection property we have 2I=\pi\int_{0}^{\pi} \frac{1}{\varphi - \cos^2{x}} dx A quick sketch (\varphi-\cos^{2}x=\frac{1}{2}(\sqrt{5}-\cos2x)) lets us deduce that...

Re: HSC 2017 MX2 Marathon What paper is that from? Looks interesting

Re: HSC 2017 MX2 Integration Marathon By considering \int_{0}^{\infty} f\left((x-x^{-1})^{2}\right) dx evaluate: \int_{0}^{\infty} \frac{x^{2n-2}}{(x^4-x^{2}+1)^{n}} dx

no need to do the last part of Q16 because it was in the 2014 BOS Trial

Last q was in a bos paper!!

BOS 2016 Trial

Re: HSC 2016 3U Marathon quick question -> If tangents have to intersect outside the parabola, then do normals have to intersect inside the parabola?

How do you even handle 15 units ;__; and how did your music composition go?

It's not about how many hours you do but the quality of them. Sounds cliche but it's really not going to help you doing questions for eight hours straight (It's said that the average can only concentrate effectively for about 30 minutes ). For me, I just did the homework exercise set everyday...

Count me in for X1 and X2 if spots are still available!

Re: HSC 2016 4U Marathon Interesting result, but do you know a method that involves using the binomial theorem? the above proof of palindromic polynomials seems too long to write in an exam given the question was two marks

Re: HSC 2016 4U Marathon yeah n sorry why i am so bad with latex

Re: HSC 2016 4U Marathon $If$ \quad a_{r} $denotes the coefficient of $ x^{r} \quad $in the expansion of$ (1+x+x^{2})^{n} \\ $show that a_{r}=a_{2n-r}

Do all the hsc past papers; if you find any topic particularly challenging/difficult try to work more on those separately by doing textbook questions. Furthermore, the topics that tend to be considered hard in extension 1 can also found in extension 2 (eg. projectile motion, counting, circle...