Recent content by Quadratic

A few of my friends and I have been trying to integrate/derive the following: f(x) = x^x without success. I'm not sure if it can be done conventionally, but I was wondering if anyone had any thoughts on this one. Thanks.

Thanks a bunch, Halls.

Just a few things that I've been thinking about lately: Are there any taylor/power series that converge to logarithmic functions (f(x)=log(x), etc.)? How would you do this? Is there any series that will graph the traditional bell curve? How would you do this? I remember the derivation...

Ahh, I see. It looks like I wrote the function down wrong (should be x^2 + x), but thanks for the insight.

Ok, I've found the answer to these questions, but I did so in more of a trial and error way. The question is: f(x) = 2x^2 + x Find the two tangent lines to the curve, which both pass through the point (2,-3). So, I tried using y=mx+b = 2x^2 + x, where m = f'(x) = 2x + 1, thus: (2x+1)x...

In this case the quadratic formula works, but for other high polynomial funtions you're probably better off with synthetic devision, factoring, and the like. For instance: (1)^4 + 3(1)^2 - 4 = 0 So: x^4 + 3x^2 - 4 = (x-1)(x^3 + x^2 + 4x + 4) = 0 (-1)^3 + (-1)^2 + 4(-1) + 4 = 0 So...

For starters, let's get the right first 2 equations. I hope you understand the following: 50 = .3x + .55y 100 = x + y y = 100 - x 50 = .3x + .55 (100 - x) 50 = .3x + 55 - .55x -5 = -.25x (-5/-.25) = x x = 20 100 - 20 = y y = 80 So it's 20 mills of 30%, and 80 mills of 55%

People are right about my sense of humour: it has 180 degree symmetry about the origin. :smile:

I'm pretty sure the US is the only english-speaking country that pronounces it as "zee". It's just like the spelling of colour, flavour, etc., and the way the word "schedule" is pronounced. When I first saw a "Lay-Z-Boy" store, I was like "... huh?". Anyway, just change the z into something like...

One time, I was just standing around in the school hallway, and I overheard three people debating over something. They eventually found that one of them was right, and the others complimented each other's efforts. I interrupted their conversation and told them that they were just like the angles...

I didn't read a page or two of this thread yet, so I'm not sure if this was touched on before, but I think that Einstein put it best in saying that reality as we know it is a persistent illusion. In other words, it can be argued that all the rules of physics, and the laws of nature in general...

The origin of "m"? Why is it that linear functions are often expressed in terms of f(x)="m"x+b? I mean, when dealing with all the other polynomials, we follow the typical f(x) = ax^n + bx^(n-1) + cx^(n-2)... so where did "m" come from? Why don't all textbooks just express it as f(x) = ax+b?

Yeah, I see what I did. Arithmetic always seems to kill me.

It's an interesting question because you sort of have to look at it in the abstract. Also, there are a few other ways to rationalize 0! = 1. For instance, if 0! was anything other than 1, the cosine function wouldn't make any sense. Consider: f(x) = Cos(x) = x^0/0! + x^2/2! -x^4/4!... where x...

First, write what you know: Initial Velocity = 19.6m/s acceleration = -9.81 Time = 1,2,3 So, from the formula d=Vi(t)+.5a(t)^2, we get: di = 19.6(1) + (.5)(9.81)(1)^2 dii = 19.6(2) + (.5)(9.81)(2)^2 diii = 19.6(3) + (.5)(9.81)(3)^2 So: di = 24.505m dii = 58.82m diii =...