1. B

    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. A

    Fully defined integrals

    Hello! So I've got this integral: And I managed to get to this result : I(n)=x^(n)(sinx)+n(x^(n-1))(cosx)—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. B

    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 π rads=180 degrees? why not π rads=1000 degrees? thanks :p
  4. S

    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.
  5. B

    Verify by induction if a formula is right for a recursively defined sequence.

    Hi, I have this exercise, and I don't know how to resolve it. Please, can you help me? Thanks! Exercise: Using the principle of mathematical induction verify if the following recursively defined sequence $\left \{ a_n \right \}_{n \in \mathbb{N}}$ $a_n = \begin{cases} a_0 =...
  6. B

    Exercise with well defined operations.

    Hi, I have some problems with an exercise where I don't understand from where some calculations come from. I post the theory part where I have some doubts, and then the correspondent exercise. Theory about well defined operations: Let S = \{a,b,c, ...\} be a set on which a binary operation...
  7. E

    Piece of spherical surface area defined by 4 geodesics

    Hello everyone, I am looking for a solution of this problem: Can somebody help me, please?
  8. M

    what bases and exponents are defined on real numbers

    I'm interested in knowing what bases and exponents have a meaning/definition in real numbers. Tell me if any of this is right. I think that $0^0$ is undefined. $ 0^a = 0 $ but only for $ a > 0 $. $b^0 = 1$ for all real $b$ except $b=0$. Is this right so far? Then we get into negative bases...
  9. J

    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...
  10. H

    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...
  11. L

    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...
  12. F

    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...
  13. P

    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 & \\...
  14. D

    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...
  15. B

    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 as follows: Area of each segment: A = ((R^2)/2)*(theta -...
  16. P

    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...
  17. B

    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...
  18. C

    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...
  19. E

    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...