Recent content by issisoccer10

Homework Statement Let {an} be a sequence with positive terms such that lim an = L > 0. Prove lim (an)x = Lx. Homework Equations If x is a real number, there exists an increasing rational sequence {rn} with limit x. A monotone sequence {an} is convergent if and only if {an} is...

No, because that would imply \sqrt{2} = -n/m, i.e. that \sqrt{2} is rational.. Thanks a lot, I really appreciate it.

Hi Dick, Thank you very much for your help. I feel that I can prove the property of rationals that your described. However, while I know that there are reals that don't have that property, such as \pi and the sqrt(1), I do not know how to prove that those two numbers do not have that...

Homework Statement Prove that there is no isomorphism, \phi, from Q under addition to R under addition Homework Equations An isomorphism \phi:Q to R is a bijection such that \phi(x + y) = \phi(x) + \phi(y), where x,y are elements of Q \phi(0) = 0. \phi(-x) = -\phi(x) The...

alright thank you.. so the constant has to be added right after the integration occurs.. I forgot about that. thanks a lot

integrating both sides gives ln(y) = ln(x)/4 = ln(x^1/4)... so y = x^1/4.. as for the inital condition, my inclination would be to plug in (2,3) into the equation... so 3 = 2^1/4 + C.. However, based on what I think it should be, instead of adding C I should be multiplying by C. But I don't know...

[SOLVED] Integrating factors or separating the variables Homework Statement The following equation can be solved by intergrating factors or by separating the variables. \frac{dy}{dx} - \frac{y}{4x} = 0 with the initial condition of y(2)=3 Homework Equations The Attempt at a...

wow...units aren't cool...actually they make everything make sense and since they make sense, all is well... anyways thanks again

if x(t) = e^{-8t} and y(t) = e^{-2t} that would work right? so differential equations are just logic? at least at this level anyways.. but as for the constant \alpha you were talking about.. that would change my parametrizations to x(t) = e^{-8t} and y(t) = 4e^{-2t} if it is to go through the...

[SOLVED] Trajectory using gradient and differential equations Homework Statement A heat-seeking particle is located at the point P on a flat metal plate whose temperature at a point (x, y) is T(x, y). Find parametric equations for the trajectory of the particle if it moves continuously in...

thanks a lot..

oh ok...so the derivative of \frac{dz}{du} = \frac{d^{2} z}{du^{2}} \frac{\partial u}{\partial x} because we really are taking the derivative with respect to x.. so basically there was another chain that I didn't see.. is that right?

[SOLVED] Chain rule problem with partial derivatives Homework Statement Suppose that z = f(u) and u = g(x,y). Show that.. \frac{\partial^{2} z}{\partial x^{2}} = \frac{dz}{du} \frac{\partial^{2} u}{\partial x^{2}} + \frac{d^{2} z}{du^{2}} \frac{(\partial u)^{2}}{(\partial x)^{2}}...

[SOLVED] Partial differential with respect to y Homework Statement Given the equation f(x,y) = (x^{3} + y^{3})^{1/3} Show that f_{y}(0,0) = 1 Homework Equations Basic chain rule.. The Attempt at a Solution Based on the chain rule...I believe that f_{y} = 1/3(x^{3} +...

wow... i feel pathetic... thanks again.