Recent content by ivanradoszyce

Hi all, I believe Conics was a topic in Extension 2 a while ago. I was just wondering if anyone had any old PDFs of Extension 2 text books that covered this topic. It more just form my personal interest that anything else. I wold really like to know how it was covered. Thanks

As a matter of interest, where does this question come from?

Here is the solution written in Latex.

Yes, that's the way I did it.

This looks very similar to the following problem: \begin{align*} \text{Given} \\ I_n &= \int \frac{x^n}{1 + x^2} dx \\ \text{show} \\ I_n &= \dfrac{x^{n - 1}}{n - 1} - I_{n - 2} \\ \text{From this expression $I_{n-2} = \int \frac{x^{n-2}}{1 + x^2} dx$ is required. }\\\\ \text{We can get...

Here is part a) and b) written in Latex. I'll post part c) soon. For c) use Vieta's formula. Attached are full solutions + a file about Vieta's formula for cubics.

This may help. The PDF was written using Latex.

The solution in Latex: \begin{align*} \text{Consider $I_n = \int_0^{\sqrt{3}}(3 - x^2)^n dx$} \\[5mm] \text{Using integration by parts } \\[5mm] u &= (3 - x^2)^n \hspace{60pt} v' = 1 \\[5mm] u' &= n(3 - x^2)^{n-1} \cdot -2x \hspace{20pt} v = x \\[5mm] I_n &= uv' - \int...

Here are a few from my favourite Year 12 Applied Mathematics book - with answers

\int \frac{1}{4 + \sqrt{x} } \, dx Let u = x^{1/2} \Rightarrow u^2 = x \begin{align*} u^2 &= x \\ \text{Differentiate both sides with respect to $x$} \\ \frac{d}{dx} (u^2) &= \frac{d}{dx}x \,\, \text{Apply chain rule to LHS} \\ \frac{d}{du} (u^2) \frac{du}{dx } &= 1 \\ 2u...

Part (c) and (d) involves Vieta's Formula for cubics. This PDF may help is solving such problems. Created in Latex.

Got it - thanks.

Thank-you very much Lith_30. I'll edit those domain restrictions to page 2.

Attached is a complete solution written in Latex

Can you please tell me where you got this question. I like it a lot!