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...
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...
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...
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...
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...
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.
\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:
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)
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)...
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...
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...
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...