# defined

1. ### May undefined values will eventually be defined?

So we know that division by zero is undefined, a lot of limiting values are also undefined. Does that mean that we will never find an answer to these questions? For example \sqrt{-1} was also undefined but we defined it. Does this mean that there is hope that someone will eventually for...
2. ### Fully defined integrals

Hello! So I've got this integral: https://prnt.sc/oc6zok And I managed to get to this result : I(n)=x^(n)(sinx)+n(x^(n-1))(cosx)â€”n(n-1){I(n-2)} However, since the integral is defined on the interval (-pi,pi) I don't know how to continue. Excuse my English for I am not a native English...
3. ### Why angles have units since they are defined by a ratio of distances?

Since \theta = \frac{s}{r} the units of s and r shouldn't cancel out? So what are radians? Also, how did mathematicians said that Ï€ rads=180 degrees? why not Ï€ rads=1000 degrees? thanks :p

Hello
5. ### Q: Let S = {x, y, z } and R be a relation defined on S such that

Q: Let S = {x, y, z } and R be a relation defined on S such that R = {(y,y),(x,z),(z,x),(x,x),(z,z),(x,y),(y,x)} Show that R is reflexive and symmetric as well.

10. ### Taylor Series for curves defined by F(x,y)=0

Hi! Given a graphic defined by function y=f(x), is possible to express f(x) like: f(x)=\sum _{0}^{\infty} \left( \frac{d^if(x_0)}{dx^i\;\;\;\;\;\;}\frac{(x-x_0)^i}{i!} \right )\Delta i BUT, and if the graphic is defined by relation F(x,y)=0, how to use the taylor series for represent the...
11. ### A function defined in R^2

Hi, First I want to apologise about my "math English" or about my English at all :D I have an exam coming soon and I am looking for help with some problems. Since no one in my univercity have time for me I will try to ask here. I hope I am posting this in the right place. Ok we have a...
12. ### Defined vs. Undefined vs. Does Not Exist

Let's take the expression \frac{x^2}{x} and its simplified form \frac{x}{1} At x=0, the results are undefined and 0 respectively. In a similar case, we can take \frac{x}{x^2} and its simplified form \frac{1}{x} Where at x=0, the results are undefined and does not exist respectively. In a...
13. ### Rotational Area defined by inequalities by Integrating

I have a question i am still struggling with after a little while browsing some other posts. It goes, The area defined by the inequalities, y ? x2 – 2x + 4, y ? 4, is rotated about the line y = 4. Find the Volume Generated. I have drawn the graph and you can see the area you are...
14. ### Spectral radius of a sparse recursively defined matrix

Let X_{N} be the 2^N times 2^N matrix as defined below. X_{N}:=\left( \begin{array}{cccccccc} A & & & & B & & &0\\ B & & & & B & & & \\ & A & & & & B & & \\ & B & & & & B & & \\ & & \ddots& & & & \ddots & \\...
15. ### Set defined by { X e P(A) | |X| is odd}

Hi, I'm having a bit of trouble understanding what kind of set the this describes: V = { X e P(A) | |X| is odd} The "e" is the "belongs to" symbol. Since A is not mentioned anywhere else, I'd say V is a set of all possible sets, that have odd number of elements in them? Is this correct? If yes...
16. ### Equal areas defined by parallel chords in a circle

Been trying to calculate multiple equal areas defined by parallel chords in a circle to mark off fuel levels on the end a horizontal cylindrical tank. Located applicable equations at http://en.wikipedia.org/wiki/Circular_segment#Formulas as follows: Area of each segment: A = ((R^2)/2)*(theta -...
17. ### Recursively defined table?

Hey guys! I have developed an algorithm to solve a certain mechanical problem (I don't want to bore you with the details...) and I would really appreciate some help by getting it into computer language. I have no skills of programming, I have done a little bit with Mathematica 8, but I...
18. ### sequences defined inductively

I'm terribly stuck on this problem. Please help! Let x_n+1= 1+1/x_n, and x_1=1. By calculating some terms, {x_2n} seems to decrease and {x_2n-1} seems to increase. Prove both of these claims by induction using the statement P_n: x_2n+2<= x_2n and x_2n+1>=x_2n-1. Show that {x_2n} and...
19. ### How to defined a probability distribution in Mathematica ?

I'm using Mathematica 7, and I need to define some probability distributions. Everything I tried, using all the Wolfram help system, failed (I really don't like their complicated and obscur "help" system). To be precise, suppose I want to define a distribution from the following normalised...
20. ### Continuity of function defined by series

There is this problem: Show that f(x)=\sum_{n=0}^\infty \left(\frac{x^n}{n!}\right)^2 is continuous in R. And here's my try: I can write f(x)=\sum_{n=0}^\infty \left[\frac{(x^2)^n}{n!}\cdot\frac{1}{n!}\right] Well, e^{x^2}=\sum_{n=0}^\infty \frac{(x^2)^n}{n!}, which converges for every x...