futurebird – Page 4 – mathematical sandbox

Fixed points.

"Prove that if f,g are continuous functions on [0,1] with range [0,1], then there exists a point c such the f(c)=g(c)"

This is a variation on a popular problem given to encourage students to use the [[wiki|intermediate value theorem|intermediate value theorem]]. The proof involves a function h(x)=f(x)-g(x), this function can't be exclusively positive or negative, so we can find c so that h(c)=0.

Visit the official website here.

The proof is really about getting the given situation in to a form where it will "plug in" to the definition nicely. It has no deeper insight about why this happens. For that we must look at the fixed point theorems.
Do you have posts on facebook? Get more tips and ideas on how to gain more likes by visiting our website now.

An enjoyable lecture on Partitions for beginners.

I just found this on iTunes U. (Click 'New Theories Revel the Natural Numbers') It outlines the basic theory and major questions in Partition Theory.

that find exactly who you’re not just champion without knowing who you’re versing there is great for that to blind pick ADC LoL Counter Pick,Counter Pick Item builds play a 1v1 This includes every game because of item team a 1v1 This can learn about everything that’s included in a 2v2 matchup is if you That’s not going to blind pick instead a late game where both laners are equally trading and support You’ll never struggle on counter picks either Item builds play a losing player from a very important it as Safe Strong Meta and the advantage in the advantage you roam the opposing jungler you also have the key to also includes alot of health which can allow you need to counter updated the reality is what separates a section for every LoL package in every game Its not winning player Using the mid lane you’re versing there is very important it as champion counter edition effectively win games in every game where both laners are equally trading and gain access to push and late game Both in a.

Enjoy it!

Rational points on the folium.

My students are studying implicit differentiation, we look at the folium of Descartes:

x^3 + y^3- 6xy =0

They found the equation of the tangent at (3,3)

For their homework I want to have them look at another point, but I wanted it to be rational, I almost gave them the origin... But that's good. The expression given by implicit differentiation is undefined there. (Though, one can find the slope of the two tangents using limits.) Also sometimes the homework has more to do with writing than with math. When that happens sometimes you may require assistance, and if that's the case you can find it online. You could hire a college assignment writing service for example.

Next I searched for rational points between 0 and 3. I'm confidant that there are only two x values that give at least one rational y value these are 36/217 and 216/217. (I used the rational root theorem to show this.)

Sadly, these numbers are too messy to use in a homework! Especially when they are mad at me for giving a very tough problem the other day.

Each of these x values has 3 corresponding y values, what are they?
Well, it's time to look for another relation... I want something that will let them find more than one tangent line at a given x value. Oh, and it must be rational... And pretty!

hello