Recent content by michalll

Hi, I was wondering if there exists an algorithm for one by one digit computation of an integer to the power of any real number? Couldn't find anything on the net.

Right.

Sorry I got it wrong, you have to determine the part of the velocity verctor that is parraler to the verctor pointing from astronaut to the airlock. Which is |\overline{v}| cos \varphi. Using |\overline{v}||\overline{u}|cos \varphi = |\overline{v}\cdot\overline{u}| you should get it.

Generally counter-clockwise is taken as positive and clokwise as negative direction

Thats easy just take into account centrifugal acceleration.

You probably have to detemine the i vector component of the astronaut's speed to hit the airlock.

Electric potencial is a path integral of electric intensity from point A to point B

The substitution used was s=x^{2}

I used McLaurin formula for e^x. The limits aren't the same but you can get back to x after integrating. The two term approximations means you use only two first terms in the sum. The sum is alternating so the error won't be greater than the absolute value of the third term in this case.

The first function is in first two aproximations always zero. For the second i would suggest \int_0^t e^{-x^2}dx = 0.5\int e^{-s}s^{-1/2}ds then approximate e^{-s} which would lead to 0.5\int \sum_0^\infty((-1)^n (1/n!)s^{n})s^{-1/2}ds which can be easily integrated

the equation for v is still valid you just have to write F in terms of x (where x is distance from the bottom part of the rope)

F is not a constant in this case, each part of the rope is beeing stretched differently depending on how close it is to the ceiling

x is only length increment not the whole lenght

I really don't know your result seems to be correct.

I think its wrong