Recent content by BustedBreaks

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...

^ If it does, I can't see it. I feel like I need to find an N in terms of e to show that this si continuous or something.

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...

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...

Well to be honest I have forgotten a lot of this stuff. I'm looking at the function (c_{1}+c_{2}sin^{2}x+c_{3}cos^2{x}) with c1, c2, and c3, as distinct constants and that all functions of this form can be combined to create another function this form. This seems to be the wrong way to think...

Show that the functions (c_{1}+c_{2}sin^{2}x+c_{3}cos^2{x}) form a vector space. Find a basis of it. What is its dimension? My answer is that it's a vector space because: (c_{1}+c_{2}sin^{2}x+c_{3}cos^2{x})+(c'_{1}+c'_{2}sin^{2}x+c'_{3}cos^2{x})...