1. S

    Proof relating to Vector Spaces

    Let V be the set of all pairs (x,y) or real numbers and \Re be the feild of real numbers. Define (x,y) + (x_{1},y_{1}) = (x+x_{1},y+y_{1}), c \cdot (x,y) = (cx,y) . Prove that V(\Re) is NOT a vector Space. I can't seem to figure out which of the 10 conditions of Vector Spaces is...
  2. P

    Finding a conjecture relating prime numbers to divisors

    Hello I was just wondering if anyone could help me find a conjecture, theorem, hypothesis around this particular result. If p,q are prime numbers, m,n are integers, and f(r) is the number of nontrivial divisors of r (ie. not 1 or r itself). That if r=(p^m)*(q^n) (p≠q) that f(r)=(m+1)n+(m-1)...
  3. A

    I need help with this question relating composite functions!

    Hi there. I am new here, and apologies if this thread is in the wrong forum. I need help with this question that I keep getting the wrong answer! Given m(x) = 15x-2 and nm(x) = 1 / 5x, x is not equal to 0, find the function of n. Any help is appreciated. Thanks!
  4. Furyan

    Question relating to the coefficients of the expansion of (2k + x)^n

    Hello, The question is: In the binomial expansion of (2k + x)^n, where k is a constant and n is a positive integer, the coefficient of x^2 is equal to the coefficient of x^3. Prove that n = 6k + 2. I got as far as: ^{n}C_{2}(2k)^{n - 2} = ^{n}C_{3}(2k)^{n - 3} I tried simplifying and...
  5. G

    Figuring out an equation relating 3 variables

    I have a practical problem that I need to set up an equation for, any help on how to do this would be really appreciated. This is the scenario- I have a tube that I am injecting fluid into at the top. After I have injected the fluid it moves down the tube at a constant speed. This fluid makes...
  6. I

    relating unkown coefficients with a known factor of a polynomial

    Hi, I think this is in the right place. I think it's also very simple but the text book I'm working from just doesn't explain it. The question is: If x + p is a factor of ax2 + bx + 3, show that p(b - ap) = 3 According to the book, I think what they want one to do is long division and then...
  7. J

    Questions relating to asymptotes

    Hello, I've just started learning about asymptotes in school. The questions I have are: 1. To find the vertical asymptote, why do you have to equal the denominator to 0? And then find x. 2. "" "" "" horizontal "" , why do you have to divide the numerator and denominator by x...
  8. R

    Question relating to solving equations with Green's functions

    An easy question hopefully. I have the solution to a differential equation y'+2ty=g(t) in the form y=\int^t_{t_{0}}g(\tau)G(t,\tau)d\tau where G(t,\tau) is greens function thus y=\int^t_{t_{0}}g(\tau)e^{\tau^2-t^2}d\tau if I want to solve it for g(t) &=t, \ 1 \leq t \leq 2 would I get...
  9. T

    PDE questions relating to Burgers equation and Power series

    Hello, I am preparing for my PDE final, and I have questions relating to two problems: My usual approach to solving PDE problems in our course (like the heat and wave equation) has been to separate the variables and then look for common solutions. However, this doesn't appear to work here...
  10. S

    Probability question relating to harmonic series

    Hello all, I'm stuck on another simple question, I think the solution is based somewhere on reversing Euler's approximation for harmonic series, yet I'm unable to make the link between the math and the question. Question: McBurgerQueen wants to run a competition where the grand prize is a very...
  11. T

    Question about a question relating to irrationality.

    So there is a problem here: That asks a person to show that e is irrational. Well, I just thought that since (for example) ...8281.. was in the string of decimals for e it had to be irrational because I was taught in elementary school that irrational numbers are those that...
  12. A

    Question relating to binomial expansion and integration

    Hi All I am working on a question where I am given (1 + x^2)^5 and asked to expand out (using binomial expansion). I have no problem with that. Then I am asked to integrate the equation for values 0 -> 0.4. No problem there. But then it asks how the estimation of the area using the...
  13. A

    Integration question relating to inverse trig functions.

    Hi, I've been doing some differentiation of inverse trig. In doing this I had to find the derivative of: arctan (3x/2) I found this to be: 6/(9x^2 + 4) To check this answer I thought I would try to integrate to see if I arrived back at the original question. However, I'm a bit...
  14. R

    Very weird question relating to critical points

    I've done some work on this, though either I've hit a strange answer or I did something wrong. The question has two parts. a) What happens to D=f_{xx}f_{yy}-(f_{xy})^2 at (0,0) for f(x,y)=x^4-2x^2y^2+y^4? Classify the critical point at (0,0). Working out the problem, I got to here...
  15. B

    Bounding probability of event relating to Poisson distribution

    Let X have Poisson(λ) distribution and let Y have Poisson(2λ) distribution. (i) Prove P (X ≥ Y ) ≤ exp(−(3 − √8)λ) if X and Y are independent. (ii) Find constants A < ∞, c > 0, not depending on λ, such that, without assuming independence, P (X ≥ Y ) ≤ A exp(−cλ). A hint says: Note that P...
  16. A

    Question relating to Markov's inequality

    I've been given a question as follows: if Y is a non-negative random variable, I want to show that P(X\geq a)\leq e^{-ta}M(t), where M(t) is the moment generating function of X. I think that Markov's inequality would be useful here, and I know that I can express E(X) as M'(0), but I'm not sure...
  17. M

    Need help with a Force question relating to Vectors

    I have no idea how to go about solving questions about forces relating to vectors, and with a test due in a few days, I don't want to go unprepared. Below is the diagram of the problem I'm having: There are several questions about this diagram, and I'd appreciate if somebody could help...
  18. R

    Integral question relating to arctan...

    How do you do this integral? \int \frac {x^2}{1+x^2} dx The original problem was \int x tan^{-1}x. By doing integration by parts, I got \int \frac {x^2}{1+x^2} dx as an integral later on. But when I try integration by parts on this second integral, I end up having to evaluate \int x...
  19. F

    Quesion on topology relating to produc spaces

    Question on topology relating to product spaces Hello: I have what may be a silly question because did not find it in the books I looked for it and is this: Is the product of closed sets closed in the product topology? The answer seems to me to be "yes".
  20. R

    Proof relating to prime numbers

    Hi I need help with this following proof. I can't seem to prove it. I believe there is something relating to coprime in this question. I have attached my question as i didn't know all the various commands to type it in latex. thanks