Interval Definition and 712 Threads

  1. N

    Spacetime interval formula - what's the d?

    I got this formula for calculating the distance between spacetime intervals at Wikipedia: ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2 Now first I thought the d was supposed to be the Greek delta which my physics teacher uses to indicate a difference of the following variable, instead of just...
  2. K

    Exploring Discontinuous Functions on an Interval [a,b]

    1. An example of a discontinuous function on an interval [a,b] that does not assume every value between f(a) and f(b). [edit] My answer to this: Piecewise function f(x)= 1/x, for x greater than and equal to -4 but less than zero (0). And f(x)=1/x for x greater than zero but less than and...
  3. S

    Interval of convergence problem

    The original series is the sum from n=1 to infinity of (n!*x^n)/(n^n) I used a ratio test to find that the interval of convergence is -e < x < e But now I need to test the endpoints, which means I need to find if the following two series converge: sum from n=1 to infinity of...
  4. D

    LUB and Nested Interval Equivalancy

    Hello there. I understand (to the best of my ability) the Least Upper Bound property and the Nested Interval property, but I don't see how the two are equivalent properties. LUB: If S \subset \mathbb{R} has an upper bound, then S has a LUB Nested Intervals: If I_1 \supset I_2...
  5. V

    Starships A & B: Relative Velocity & Time Interval

    suppose there are 2 starships, A and B, moving towards each other wuth a relative velocity of 0.999c. they pass each other at time t=t0. after moving a certian distance (relative), they stop(relative to each other), turn around and again statr moving towards each other with the same velocity, of...
  6. K

    Proving f(x) intersects a graph when given an interval

    Hi, Does anyone here have any pointers on how to even start the following question? Suppose for all x element [0, 1] we have f(x) element [0, 1]. Prove that the graph f(x) must intersect the line y = 1 - x Any help would be great thanks.
  7. D

    Series (finding the interval of convergence)

    \sum _{n=1} ^{\infty} \frac{x^n}{3^n} = \sum _{n=1} ^{\infty} \frac{x}{3} \left( \frac{x}{3} \right)^{n-1} = \frac{\frac{x}{3}}{1-\frac{x}{3}} = \frac{x}{3-x} \textrm{How can I obtain the interval of convergence of the given series? Thanks.} :smile:
  8. R

    Interval with the leingth of 3

    f(x)=x^2-2x+2 Draw the function (I can do that) and deside an interval with the leingth of 3, there by f illustrates on an interval in the leingh of 25/4. (how??) (hope you can read it, I am from Denmark, so i'll try)
  9. J

    Proving Convexity of a Function on an Open Interval

    Hello, how can I proof this: given: a convex function on an open interval I,which is a subset of R. I have to show that the function can be differentiated on the whole interval. I already proved the following for a<b<c, a,b,c in I: f(b)-f(a))/(b-a)<(f(c)-f(a))/(c-a)<(f(c)-f(b))/(c-b)...
  10. R

    Solve for x algebraically in the interval 0<x<2pi sin2x + 4sinx = cosx + 2

    Hello, I am in grade 12 taking math31 which is pretty much a college course. I am not doing that great in it at the moment and I just found this forum with less than 2 months left in the semester. Anyway, there are a few questions I am stuck on. One of them is: (note: all of the '<' are...
  11. S

    Definition of relativity's interval

    Definition of relativity's "interval" Okay I have Kip Thorne's text in front of me that says the following: If (\Delta s)^2 > 0 the events are called spacelike If (\Delta s)^2 = 0 the events are called lightlike If (\Delta s)^2 < 0 the events are called timelike Then I have David W...
  12. C

    Proving that a sequence is confined to a certain interval

    In class we were given the following sequence- (0,1 1/2, 3/4, 1 1/8, 15/16, 1 1/32 ...) So it's alternating about zero. We're told then that given any number a>1 it s true to say that the sequence (xn) is eventually confined t [0,a] We now have to prove this... Inworked out the...
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