Well, what I was trying to say was that the upper sum cannot equal 0 because for any interval [a,b] M will not be 0 because there is always an irrational greater than 0 no matter how small the partition [Xo, X1] gets. Because M will never be 0 the inf of the Upper Darboux Sums will never be 0...
Let f:[0,1] be defined as f(x)= 0 for x rational, f(x)=x for x irrational
Show f is not integrable
m=inf(f(x) on [Xi-1, Xi])
M=sup(f(x) on [Xi-1, Xi])
Okay so my argument goes like this:
I need to show that the Upper integral of f does not equal the lower integral of f
Because...
So I've been trying to figure this out. The question is:
If the limit x->infinity of Xn=Xo
Show that, by definition, limit x->infinity sqrt(Xn)=sqrt(Xo)
I'm pretty sure I need to use the epsilon definition.
I worked on it with someone else and we think that what we have to show is the...
hi, I have two equations that I have used the Solve function in Mathematica to solve for A in both equations
What I am having trouble with is trying to equate the results and solving for another variable J automatically
Basically this is what I want to do:
Solve[Eqn1, A]
It gives {{A ->...
This may be a dumb question, but I just want to make sure I understand this correctly.
For R_{1}, R_{2}, ..., R_{n}
R_{1} \oplus R_{2} \oplus, ..., R_{n}=(a_{1},a_{2},...,a_{n})|a_{i} \in R_{i}
does this mean that a ring which is a direct sum of other rings is composed of specific elements...
I'm trying to solve this equation:
Ux + Uy + U = e^-(x+y) with the initial condition that U(x,0)=0
I played around and and quickly found that U = -e^-(x+y) solves the equation, but does not hold for the initial condition. For the initial condition to hold, I think there needs to be some...
The problem statement is:
Solve the Neumann problem for the wave equation on the half line 0<x<infinity.
Here is what I have
U_{tt}=c^{2}U_{xx}
Initial conditions
U(x,0)=\phi(x)
U_{t}(x,0)=\psi(x)
Neumann BC
U_{x}(0,t)=0
So I extend \phi(x) and \psi(x) evenly and get...
I'm following an algorithm my teacher gave us and I'm trying to understand it...
I'm trying to solve this PDE 2Ux-Uy+5U=10 with U(x,0)=0
First I need to solve the homogeneous equation.
So I set up the relation:
V(y)=U(2y+c, y)
to solve 2Ux-Uy=0
where the characteristic equation is y=1x/2...
Consider heat flow in a long circular cylinder where the temperature depends only on t and on the distance r to the axis of the cylinder. Here r=\sqrt{x^{2}+y^{2}} is the cylindrical coordinate. From the three dimensional heat equation derive the equation u_{t}=k(u_{rr}+\frac{u_{r}}{r}).
My...
Okay so I get your method here and I am trying to apply it to this one (23)(13) but I am not getting the answer the book has which is (123)
I set it up like this
(23) (13)
123 123
132 321
then
so 1 goes to 3 then 3 goes to 2, 2 goes to 2 then 2 goes to 3, 3 goes to 1 and 1 goes...
I am having trouble understanding this example:
Let G=S_3 and H={(1),(13)}. Then the left cosets of H in G are
(1)H=H
(12)H={(12), (12)(13)}={(12),(132)}=(132)HI cannot figure out how to produce this relation:
(12)H={(12), (12)(13)}={(12),(132)}=(132)H
I understand (12)H={(12), (12)(13)} but...
To give a bit more context.
I was trying to solve the partial differential equation: 3U_{y}+U_{xy}=0 with the hint, let V=U_y
substituting we have 3V+V_{x}=0
then -3=\frac{V_{x}}{V}
I didn't really know how to continue from here so I just played around and figured out that V=e^{3x} and...
So in doing a homework problem I have convinced my self that \int\frac{V_{x}}{V}=ln(V) which I vaguely remember learning in class, but I'm having trouble deriving it. Can someone help me out?
I see what you mean by the difference in functions, however I feel like they would have written it the way you did, {1, sin2x, cos2x}, if that's what they meant? They way I see it, the function in the question represents all functions of that form which is why they have function plural.However...