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Like I illustrated after that, you take the limit of the x value where the open circle should be, in this case we take the limit of x=-2 because the open circle is at x=-2. If it was at x= k then we take the limit of x=k of the function. When we get a pair of coordinates in this case (-2, 1/4)...

\frac{2^{m-3}}{(3 \times 5)^{-m-1}} \times \frac{(2\times3)^{2-m}}{5^{m+1}} =\frac{2^{m-3} \times 2^{2-m} \times 3^{2-m}}{3^{-m-1} \times 5^{-m-1} \times 5^{m+1}} =\frac{2^{-1} 3^{2-m}}{3^{-m-1} \times 5^0} =\frac{1}{2} \times 3^3 \\ = \frac{27}{2}

English really isnt that hard to be honest, you just dont want to fall into a trap of roting essays and such. Its much easier for someone to just know their text really well and write what they know in the exam, with enough practise and knowledge of your own ideas really well, you can answer...

Also I was meaning to post this, but I kept forgetting, but here it is: Slant Asymptote You should check out some of his other videos, he is very clear and concise as well (Id post the curve sketching one but it involves calculus in it)

Re: HSC 2012 Marathon :) The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle. Difficulty: Moderate Lets revive this thread

Using the integrating with respect to y method: y=\ln x \\ x=e^y \\ \\ dx=e^y dy \\ \therefore \int \ln x \ dx= \int y e^y dy (though that this bordering on 3U integration) So it seems that you do need to do integration by parts You could do the substitution u=ln y But that leads you to...

Oops. Yeah I should probably be more careful when doing questions especially when Im uploading on bos Sorry guise

Solution Obviously, if you want to do this yourself then dont look at the solution.

Look at the function again: y=\frac{x+2}{(x+2)(x-2)} The graph cannot be at x=-2 AND x=2. The point is, at x=2 there is an asymptote, but x=-2 there is no asymptote because it cancels out with the numerator, the only alternative is an open circle. To find the y-coordinate of the open...

Dont mind her

Re: The p00n thread Counter Strike Global Offensive is great

post count farm

Oh, sorry guys..

But cant we just do this for AM-GM (my knowledge of this inequality is a 2 min google search and I found that it is an inequality) (\sqrt{x}-\sqrt{y})^2 \geq 0 \\ \\ x-2\sqrt{xy}+y \geq 0 \\ \\ \frac{x+y}{2} \geq \sqrt{xy} Is this not axiomatic enough? (Im missing something I think)

Agreed.

Ok so are you going to believe the crapload of information that comes from media personality? I don't mean from celebrities, I mean the stupidity coming off people who call themselves educated. Being able to analyse what your seeing, the information people tell you, its important to form your...

But literature is just another form of another person in real life conveying their views on the world (if you read good texts). That might sound cheesy, but its the truth. For example in Harry Potter it may not be very evident but there is alot of Biblical Imagery which is reflective on...

Of course I don't blame any student for their poor English experience, there is an extreme shortage in supply of good english teachers who know how to teach the course and know how to mark essays and such. Im lucky to have a good teacher... My teacher has taught me to speak and write more...

I frequently refer to different philosophies and historical contexts and that's what separates my essays from the conventional 15/20s and such. I don't know how easy your school might mark though. At my school to get 90s you need to do more than just regurgitate frequently used ideas and...

Referring to my post about mathematicians and scientists. The good mathematician knows how to explain his proofs in elegant way so that anyone can understand it. Your going to need to know how to talk and write elegantly such as for a university thesis and such