Search results

Re: MX2 Integration Marathon Hence \int \sin (\ln x) \ dx

Re: HSC 2014 4U Marathon - Advanced Level Is cross-product formula Heron's formula? If not the alternative would be Heron's formula which is quite easy to prove

Re: HSC 2014 4U Marathon - Advanced Level Yep

Re: HSC 2014 4U Marathon - Advanced Level \\ $In 3D space consider the points$ \ \ A(a,0,0) \ , \ B(0,b,0) \ , \ C(0,0,c) \ , $and$ \ O(0,0,0) \\ \\ $A tetrahedron is formed with these 4 points$ \\\\ $Let$ \ d \ $be the distance from$ \ O \ $to the triangle$ \ ABC \\ \\ $By considering volumes...

Re: MX2 Integration Marathon \int \sin (\ln x) + \cos (\ln x) \ dx

Re: MX2 Integration Marathon All of them seems good to me

Re: MX2 Integration Marathon There you go mate \lim_{N \to \infty} \int_{-N}^N \frac{dx}{(x^2+a^2)(x^2+b^2)}

Re: MX2 Integration Marathon \int_{-\infty}^{\infty} \frac{dx}{(x^2+a^2)(x^2+b^2)}

Re: HSC 2014 4U Marathon Bump

Re: HSC 2014 4U Marathon Rather \\ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \\ \\ $or$ \\ \\ \frac{y^2}{b^2} - \frac{x^2}{a^2} = 1 Which are both hyperbola

\\ $Consider the general line through$ \ \ P(\alpha, \beta) \ \ $of the form$ \\ y=mx+c \ \ $intersecting the ellipse at$ \ \ (x_1,y_1) \ ,\ (x_2,y_2) \\ \\ $We find that solving for the intersections (of which$ \ P \ $is midpoint of)$ \\ \\ x^2(b^2+m^2a^2) + 2mca^2x + a^2c^2 - a^2b^2 = 0 \\...

Re: HSC 2014 4U Marathon Its built into the site, its called LaTeX. To use it you use tags like [.tex] and [./tex] (without the dots). So [.tex] \frac{5}{3} [./tex] Becomes \frac{5}{3} To get a good grasp of the latex language, you can use the buttons here And then copy paste the...

Re: HSC 2014 4U Marathon fixed

Re: HSC 2014 4U Marathon \\ $Sketch the lines$ \ \ y=4-k, \ \ y=k-6 \ \ $the part of the plane where 1 function is positive and the other negative, the curve is a hyperbola, rejecting function values where both functions are positive or negative, hence$ \\ \\ k<4, \ \ k>6

Re: HSC 2014 4U Marathon Perhaps the domain co-domain question was a little too far, but I'm pretty sure every other question was a pretty decent level

Re: HSC 2014 4U Marathon \\ $Prove that for the real polynomial$ \\ \\ a_0 + a_1x+ \dots +a_nx^n \\ \\ $The expression can only be equal to 0 across all$ \ x \ $if and only if$ \\ \\ a_0=a_1= \dots = a_n = 0

Re: MX2 Integration Marathon \int \frac{dx}{1-e^{kx}} \ dx = \int \frac{e^{-kx}}{e^{-kx}-1} \ dx = \frac{-1}{k}\ln |e^{-kx}-1| + c ------------------------------------------------------- \\ $Find$ \ \ I_n = \int_0^{\pi} e^{x} \sin^{2n}x \ dx

Re: HSC 2014 4U Marathon To be fair they are very easy for MATH1901 lol ---------------------- \\ $In the complex plane consider the points$ \ A,B \ $represented by the complex numbers$ \ z,w \ $respectively$ \\ \\ $Another point$ \ C \ $represented by the complex number$ \ v \ $divides$ \...

The issue is the limit of the function at zero, which cannot be seen graphically

\int \frac{1}{x} \ dx = \ln(x) + c = \log_e(x) + c\ \ \ $always$