Search results

Re: HSC 2013 3U Marathon Thread (if its a definite integral) Well yes you do use it but I wouldn't call it a 4U technique..... (or is it? I don't know what is said in the 4U syllabus)

Re: HSC 2013 3U Marathon Thread Can someone do this version anyway? What I got was: If we take the number of arrangements of n couples around a round table so that no couple is together as u_n Then we need to find: u_4 To find u_4 , I considered an already set up u_3 arrangements of...

Re: HSC 2013 4U Marathon $Prove that for positive integers$ \ \ n \left(\frac{n+1}{2} \right)^n \geq n! $You may not use the inequality$ \sum a_k \geq \left( \prod a_k \right)^{1/k}

Re: HSC 2013 3U Marathon Thread Yea I'm not sure why I wrote a different word to what I was thinking of Dat English in 6 days

Re: HSC 2013 3U Marathon Thread Yep I already had this explained to me, Would a generalization to n couples be hard to do?

Re: HSC 2013 3U Marathon Thread Yep, once again my bad haha

Re: HSC 2013 3U Marathon Thread $ Using the substitution$ \ \ u= \frac{1}{x} \ \ $Show that$ \int_{1/2}^{2} \frac{\ln x}{1+x^2} \ dx = 0

Re: HSC 2013 3U Marathon Thread Oh ok, my bad

Re: HSC 2013 3U Marathon Thread The answer is 12 apparently lol

Re: HSC 2013 3U Marathon Thread $How many ways are there to arrange 4 married couples around$ $ a round table so that no person is seated next to their partner?$ Disclaimer: I can't do this

Re: HSC 2013 2U Marathon $The line$ \ \ y=mx \ \ $is tangent to the curve$ \ \ y=\ln x $Find$ \ \ m \ \ $and hence find the area of the region bounded by the line, the curve and the$ \ \ x$-axis$

Re: HSC 2013 2U Marathon Hm, was this your expression: \int_1^n \frac{1}{x} \ dx< \frac{1}{2}\left(1 + \frac{1}{n} 2\left( \frac{1}{2} + \dots + \frac{1}{n-1} \right) \right) ?? That is what I got initially

Re: HSC 2013 4U Marathon $A function can be expressed as $ f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!}x^n $Where$ \ \ f^{(n)} (x) = \frac{d^n}{dx^n} f(x) \ \ f^{(0)}(x) = f(x) $Express$ \ \ e^x \sin x \ \ $in this form$

Re: HSC 2013 2U Marathon $Consider the graph$ \ \ y= \frac{1}{x} \ \ $two points$ \ \ A\left(a,\frac{1}{a} \right) \ \ $and$ \ \ B\left(b, \frac{1}{b} \right) \ \ $lie on the graph$ $i) Show that the straight line$ \ \ AB \ \ $is above the hyperbola$ \ \ \ \fbox{1} $ii) Use the trapezium...

Re: HSC 2013 3U Marathon Thread Says the guy who takes 10 minutes to write 2 lines of latex

Re: HSC 2013 2U Marathon No latex 2/10 ----- $ Find the number of solutions in$ \ \ x \ \ $to the equation$ \ln(x+1) = mx

Re: HSC 2013 4U Marathon f(x) \ \ $is an increasing function over all x reals$ \ \ f(2013) = 2013 $Describe the graph of $ g(x) = \frac{af(x) +b}{cf(x) + d} \ \ $for$ \ \ ad = bc

Re: HSC 2013 2U Marathon $i) The point$ \ \ \left(p,q \right) \ \ $lies on the curve$ \ \ y = \frac{1}{x} \ \ \ $show that$ \ \ q = \frac{1}{p} $ii) Show that the tangent to the curve at$ \ \ (p,q) \ \ $is given by$ \ \ x +p^2y = 2p $iii) This tangent cuts the$ \ \ x \ \ $and$ \ \ y \ \...

Re: HSC 2013 3U Marathon Thread $i) Use the substitution$ \ \ u = \sin x \ \ $to evaluate$ \int_0^{\pi /2} \sin^{2k} x \cos x \ dx = \frac{1}{2k+1} $Hence evaluate$ \int_0^{\pi /2} \cos^{2n+1} x \ dx $Hence by substitution find$ \int_0^{2} x^{2n} \sqrt{4-x^2} \ dx

what if carrot was jkwong