Recent content by Gackhammer

Hey guys, I have a question for you... how would one go about solving an equation like this... or this... This came across my mind the other day. I was wondering how to solve that equation if the function is of t-1, instead of t. Obviously, if it was f(t), the solution would be Ce^t, but I was...

Hey So, I was wondering how to convert from one coordinate axes to another... in particular, where the new axes are y = x and y = -x, as seen by the picture below I want it so that the Red dot in the new coordinate system will be (\sqrt2,0). Is there an easy way to do this? (My lookings on...

So what you are saying is ... For input n = 1,2,3,4,5... a_n = 1,2,1,2,1,2There are a number of ways you can do this (click on Equations for Links )... 2- n mod(2) 2-[sin^2(\frac{\pi n}{2})]Just a couple that I thought off in my head... One is discrete, one is continuous

So, just wanted to make some other interesting points (on the damping point i mentioned in the first post) So here's the equation x^2 -4x-9, with an input of 1. For the recurrence equation x = \frac{9+4x}{x}, here is the plot of number of recurrences (n = 1,2,3) and the value it produces...

Is there a general equation of damping? I know that there is a second ODE for damping with regards to springs, and with RLC circuits, but is there a general form of damping equations (with critical-damp, overdamp, and under-damp). I know how to solve second ODEs, but I was wondering if there was...

Thanks! I will!

So I have been thinking of this problem... what is the greatest rate of angle change for a function? As in, what is the point in which a function achieves its greatest rate of angle change... Well, the angle of a function can be determined by arctan(y') The Rate of Angle change is...

Just Thought this would be cool to share with yall So say you have two functions, B(x) and A(x) The equation [SIZE="5"]\frac{b(x)+a(x) + (b(x)-a(x))sin(nx)}{2} Will give you a sin wave in between these two functions (I was playing around with this and finally figured out the equation a...

As long as you mean g(f(x)) and w(g(f(x))), then you have the right answer

Ʃ(1/2^k) from k = 1 to infinity

Well here's something that might help (or not) I did something with interative sums (liek 4 + 5 + 6, or 12+13, or 23+24+25+26+27) that always differ by one (and only integers) So for 23, the only iterative sum is 11 + 12 For 26, its 5+6+7+8 Its basically related to the factors of the...

So, I am trying to make up this theory of trying to solve any equation ever using recurrences... Ill show you what I mean Consider the quadratic function - f(x) = x^2 - 3x + 2 Well, obviously you could do this the easy way and do factoring and figure out x = 2 or 1... no big deal right? But...

f'(x) = 3f(x) lets say y = f(x) for funsies y' = 3y (dy/dx) = 3y dy/(3y) = dx Integrate with respect to both sides... right side = X+ C Left side, , it equals (1/3)*(lny) (technically absolute value of y, but whatevs) so ln(y) = 3x + 3c ... which we can also say 3x + C, since C...