Recent content by Mathoholic!

Yes, I know that. My problem is knowing which differential segment dx to choose on the line (if this makes any sense). And I'd like to solve this problem from the point of observation of any point (x,y) in the plane. :/

Homework Statement A finite line of charge (L=L1+L2) with a linear density of d(x)=k.x, in which k>0. This finite line goes from -L2 to +L1 in the x axis. Calculate the electric field and the electric potential in the point P=(0,H). Homework Equations dV=(1/(4*pi*ε0))*dq/r The...

I'm familiarized with finding limits of most kinds of functions. I was struck by a problem: What if the variables of the function belong to different sets of numbers? My point being, given the function: f(n,q)=\frac{n}{q} With n belonging to the set of natural numbers and q belonging to the...

1Are you saying that I can only fully convert heat into work in a irreversible process? I'm not sure I can give much more detail about the system. I've already given all there's to know about the problem. I'm having trouble getting the definitions of reversible process and irreversible...

The problem is: Having three bodies with thermal capacities (C) as sources of heat to a heat machine, what is the maximum work I can extract from this system, given that the bodies are at temperatures T3, T2 and T1 (T3>T2>T1), leaving them at an equal final temperature? I tackled this...

Thanks, I've got it know :)

Homework Statement The exercise asks you to calculate the magnitude of the magnetic field (\vec{B}=B\hat{z}), knowing that the U shaped conductor is initially parallel to Oyz plane and then rotated around the y-axis to a stable position defined by θ (angle) with the vertical axis (z). The U...

Homework Statement It is given a set defined as: 0≤x≤1, 0≤y≤1-x. With x,y in ℝ. f(x,y)=1 (plane parallel to Oxy plane) They ask you to express the integral ∫∫Setf(x,y)dxdy in polar coordinates and calculate it. Homework Equations x=rcosθ y=rsenθ r=√x2+y2 The Attempt at a...

No, I haven't. I'm at the first year of physics degree. I have no idea of when I'll learn KKT conditions .-.

So, let's see if I got this right: I have a function f(x,y) with its graph in space: (x,y,2x3-2y3-3x2). If they hadn't give me the restriction K, the only two candidates to maximum and minimum would have been the (x,y) pairs for which ∇f(x,y)=(0,0), which are (0,0) and (1,0). When they...

Homework Statement f(x,y)=2x3-2y3-3x2 K={(x,y)\inℝ2:x2+y2≤5,y≤0} Find the maximum and minum of f(x,y) within K. Homework Equations ∇f(x,y)=(6x2-6x,-6y) Hess(f)=diag(12x-6,-6) (relevant?) The Attempt at a Solution What I've done so far was calculate the pair(s) (x,y)...

Homework Statement The function is: f: D={(x,y)\inℝ2:x+y≠0}→ℝ (x,y)→\frac{x-y}{x+y} They ask you to prove that the limit as (x,y)→(0,0) is non-existent. Homework Equations The Attempt at a Solution My attempt at a solution was using the definition of limit: If there was a...

When I rewrote the expression in polar coordinates it gave the following: f(r,θ)=rcos3(θ) When (x,y)→(0,0) , r→0, with r=(x2+y2)1/2 Then f(r,θ)→0 when r→0. Am I doing this right?

Can I prove that the function is continuous by using the composition of functions like so(?): g(t)=(t,t) fog(t)=\frac{t}{2} with t\neq0 fog(t)=0 with t=0 Given that g(t) is continuous and fog(t) is continuous because when t→0, fog(t)=0.

Homework Statement To study the continuity of a function with two variables (x,y). Homework Equations f(x,y)=\frac{x^3}{x^2+y^2} if (x,y)\neq(0,0) f(x,y)=0 if (x,y)=(0,0) The Attempt at a Solution I've tried going by the composition of functions but I can't seem to get anywhere...