Hey,
I am not really versed in differential equations myself, so I should apologize beforehand in case my comments are utterly irrelevant to the problem at hand. As you said, the function has spherical symmetry - and therefore, the most sensible thing to do, in my opinion, would be to...
Hey,
Since I can't quite browse the book (assuming such function should be available), could you possibly post here the solution provided? Furthermore, and I ask as I'm not very acquainted with the notation used, are you asked to solve for z = z(x), y = y(x)? If that is the case, how about y =...
As for #2,
Note that the total work done on the body, equals the change in its *kintetic energy*. In your case, since the ball remains in constant speed, its kinetic energy is obviously unchanged. Moreover, considering the fact that gravity did do work on the ball, its potential energy would...
Hey there,
A possible derivation of the sum requested uses the telescoping series property.
Note that for every j, Aj can be expended to -
Aj = j / ( j + 1 )! = 1 / j! - 1 / ( j + 1)!
Summing over 1,...,n would then yield the desired result.