Recent content by Vanrichten

Ahh thanks, now I fully understand this...Integrating the left hand side gives 1/2mV^2 which can be evaluated from the initial to final position right? And then the kinetic energy is equal to the work done

Hmmm,that makes some sense but I'm not sure I have the intuition to know WHY it's hidden. Is this always the case?

Thanks, this made things a bit more clear. I've done more research on the chain rule and I think I'm starting to understand. The correct term for this is In Leibniz notation, if y=f(u) and u=g(x) and are both differentiable functions, then dy/dx = dy /du du/ dx For my particular case, you...

Hello, I'm new to the language of calculus. I am learning about Newtons second law and I'm trying to understand it's forms in calculus. Excuse my notation, just trying to keep it as simple as possible. F=m * dV/dt I know V= dx/dt My textbook says you can 'apply chain rule' to obtain the...

Ok so i have the equation y'=y^2(y-3)(y-5)^3 I found the equilibrium positions to be y=0, y=3, y=5. For my phase diagram all the arrows are pointing up so the solutions are nodes? The last part asks Describe the long term behavior of the solution to the above differential equation with...

That makes perfect sense ! Awesome thank you so much.

So, how would I rewrite this? I'm not really sure =/

In this problem I have drawn out the region specified and noticed two sets of parallel lines indicating to me that a change of variable(u and v) are able to be used to solve this integral. I decided that u=y-x and v = -2x-y then solving for x and y I obtain x= (u-v)/3 and y = (4u-v)/3 From...

I have the region r = 2 + cos(theta) . I know the area should be 18.64. I set it = 0 and then solve for theta. So theta = 0 and theta = 2pi I set up my integral [0, 2pi] 1/2(r)^2 dThetaA After simplification I got 1/4 integral cos2theta + 4costheta + 5 but my answer does not come out right...

I think I got it. Could you verifiy I have the correct change of variable now, I got x = (u-v)/3 and y = (4u-v)/3

Ok the first problem is The output Q of an economic system subject to two inputs, such as labor L and capital K, soften modeled by the Cobb-Douglas production function Q(L;K) = cLaKb, where a; b and c are positive real numbers. When a+b = 1, the case is called constant returns to scale. Suppose...