Recent content by Lee33

Nope, I was just confirming. Thanks for confirming!

Homework Statement Show that if ##f## is a continuously differentiable real valued function on an open interval in ##E^2## and ##\partial^2f/\partial x\partial y=0,## then there are continuously differentiable real-valued functions ##f_1,f_2## on open intervals in ##\mathbb{R}## such that...

Homework Statement Given a line ##l## and a point ##B\in l## in a protractor geometry, there exists a unique line ##l'## that contains ##B## such that ##l\perp l'.## Homework Equations None The Attempt at a Solution I am not sure how to prove uniqueness or existence in this...

By l'hopital we have that \lim_{x \to 0} \frac{xy}{x(|x| + |y|)} = \frac{y}{|y|} Is that correct? The absolute value is throwing me off if I am wrong.

Hm, let's see if I understand your reasoning because I am a bit confused. ##\lim_{y \to 0} \left.\frac{\partial f}{\partial x}\right|_{(0,y)} = \lim_{y \to 0} \frac{f(x,y)}{x}## which does equal ##\left.\dfrac{\partial f}{\partial x}\right|_{(0,0)}##. Am I correct on that?

Homework Statement Where is the function ##f:E^2\to\mathbb{R}## given by ##f(x,y)=\begin{cases}\frac{xy}{|x|+|y|} & , \ \text{if} \ (x,y)\ne(0,0)\\ 0 & , \ \text{if} \ (x,y)=(0,0) \end{cases}## differentiable? Homework Equations None The Attempt at a Solution The function is...

Thank you very much!

Collinsmark - Following your advice will ##I_2## be ##7##?

So it should be positive ##15## since the direction is in the positive direction?

So will ##I_2## equal ##-15##?

Homework Statement Write the node equation for the circuit in the figure. If ##I_1 = 6 A,## ##I_4 = 5 A,## and ##I_3 = 4 A,## what is the value of the outward-going current ##I_2##? Homework Equations None The Attempt at a Solution I know that in the steady state, the electron...

I am not sure what exactly to do. Can you elaborate further please?

Homework Statement Let ##[a,b]## and ##[c,d]## be closed intervals in ##\mathbb{R}## and let ##f## be a continuous real valued function on ##\{(x,y)\in E^2 : x\in[a,b], \ y\in[c,d]\}.## We have that ##\int^d_c\left(\int^b_af(x,y)dx\right)dy## and ##\int^b_a\left(\int^d_cf(x,y)dy\right)dx##...

Homework Statement Conventional current flows in a ring in the direction indicated in the diagram (if you stand at location A, on the +x axis, and look toward the ring, current flows clockwise). At each of the locations labeled by a letter, use the right hand rule to find the direction of...

Opps. I meant A instead of C. I have edited the post. Sorry about that.