Recent content by find_the_fun

Dividing by the entire duration of the video or up to the point watched?

In a paper I'm reading the author keeps using the word "normalized". What does it mean?We use playback interruption time as our main metric. However, since the viewed length by a user varies widely, instead of just measuring total interruption time of each view, we normalize it by the viewed...

I'm a little stuck getting started on this question. y''+\tan(x)y=e^x with y(0)=1,y'(0)=0. I know the existence and uniqueness theorem for an nth order initial value problem How do I apply the theorem?

I hate to ask this but whenever applying a function to the equation, the arguments is the entire one side of the equation right? What I mean is ln|y|=ln|x|+C can be rewritten as e^{ln|y|}=e^{ln|x|+C} but not e^{ln|y|}=e^{ln|x|}+e^C ? So the entire RHS or LHS becomes the argument? Similarly...

is e^{2 \ln{|x|}} = |x^2| or x^2?

This is what I was trying to explain in this http://mathhelpboards.com/chat-room-9/science-vs-philosophy-9353.html about how when science finds something, other subjects yield to it or at least in the sense that when one piece of established science changes everything built on top of it must change.

Given \frac{dy}{dx} =2xy^2 and the point y(x_0)=y_0 what does the existence and uniqueness theorem (the basic one) say about the solutions? 1) 2xy^2 is continuous everywhere. Therefore a solution exists everywhere 2) \frac{\partial }{\partial y} (2xy^2) = 4xy which is continuous everywhere...

Thanks I get what you're doing. But how do you get from 4+4\left(x^2-x-1\right)\ge0 to 1+x^2-x-1\ge0 ?

I think I get the idea but am a little stuck on how to express it as a quadratic. So y=1 \pm \frac{\sqrt{1-4(1)(-1)}}{2(1)}+2y EDIT: what exactly do you mean express as a quadratic?

What is the domain of y^2-2y=x^2-x-1? I don't know how to find it for implicit functions.

For some reason every time I take an environmental science class the prof has a bone to pick with the scientific principle. Last lecture he stated that "people think that theory is based on observations but this is wrong, what people observe is based on theory". He also made the point about how...

Isn't it because interval has to be continuous i.e. can't have a break at 0?

The question is solve, give transient term and interval of solution for x \frac{dy}{dx}-y = x^2 \sin{x} and the answer key has y=cx-x\cos{x} and (0, \infty). Why wouldn't the interval be (-\infty, \infty)?

I forget but I think I had fouled up at an earlier step than shown.

Maybe the video was aluding to L'Hôpital's Rule when it said e^t grows faster than t. By the way, according to here \frac{\infty}{\infty} is indeterminate.