Recent content by duarthiago

Thank you for your insightful answer. About the exercise, I'm not sure, but it seems that ##y## goes through (0,##\delta##) and (##\delta##,0). Then ##x^3## (which also lies on the circle) will be greater than ##\delta - x## at some point, so the sign of the denominator becomes negative. ##y##...

Well, I worked a little bit more on the problem and polar coordinates wasn't necessary. Taking a curve like ##\gamma (t) = (\sqrt[3]{t-t^2},t)## is enough. About my second question: now is quite clear that if I choose a curve that goes through the origin, then I have to study what happens when...

Homework Statement Evaluate ##lim_{(x,y)\to(0,0)\frac{xy}{y-x^3}}## Homework EquationsThe Attempt at a Solution I've tried move towards the origin along the path ##\gamma_{1} (t) = (t,2t^3)##, which leads to ##2t=0##. Then I've tried to use ##\gamma_{2} (t) = (0,t)## which leads to...

Of course! I didn't even try to see an integration by parts there. Thank you!

I've just found the following example on Piskunov: \int \frac{t^2 dt}{(t^2 + 2)^2}\\= \frac{1}{2}\int \frac{t d(t^2 +2)}{(t^2 + 2)^2}\\=-\frac{1}{2}\int t d(\frac{1}{t^2 + 2})\\=-\frac{1}{2}\frac{t}{t^2 + 2}+\int \frac{dt}{t^2 + 2}\\=-\frac{t}{2(t^2 + 2)} + \frac{1}{2...

Very well! Thank you everyone.

I don't know about ##v_{0}##, the book seems quite clear about it be the velocity of the ejected material, although what you said fits with the diagram that I have here, with ##v## being the velocity of the air entering the engine. So what is happening is that the change of velocity of air which...

I've read that the total forward force on an engine is given by a change of momentum which is written as ##P = \mu_{fuel}v_{0} + \mu_{air}(v_{0}-v) ##, where ##\mu_{fuel}##, ##\mu_{air}##, ##v_{0}## and ##v## are respectively the rate of decrease of mass of the fuel being burnt, the rate which...

I'm a second year physics student and since last year I've been noticing that an old habitis becoming a serious problem: when I can't solve some exercise in a set, I literally can't do anything with respect that subject until I solve it. It has became something quite similar to an OCD. I already...

Oh, of course, it would be something like a piecewise function where x \sqrt{3} if 0 \leq x \leq \frac{a}{2} and a \sqrt{3} - x \sqrt{3} if \frac{a}{2} < x \leq a. Thank you for your answer.

Please let me ask: I think I understood why the upper term from integration interval is equal to x\sqrt{3}, is the height in function of x, but what is the idea behind the upper term from \int_0^{\sqrt{3}(a-x)} x \ dy?

Hello everyone, I'm Thiago, a physics student and a hobbyist programmer. I'm currently interested in molecular dynamics simulation and astrobiology. I'm also fairly interested in animation applied to visualization of molecular processes. By the way, the Physics Forum threads often helps me with...