Recent content by The-Mad-Lisper

Only after the fact, I managed to modify Nicole Oresme's proof of the divergent nature of a harmonic series.

Homework Statement \sum\limits_{n=1}^{\infty}\frac{n-1}{(n+2)(n+3)} Homework Equations S=\sum\limits_{n=1}^{\infty}a_n (1) \lim\limits_{n\rightarrow\infty}\frac{a_{n+1}}{a_n}\gt 1\rightarrow S\ is\ divergent (2) \lim\limits_{n\rightarrow\infty}\frac{a_{n+1}}{a_n}\lt 1\rightarrow S\ is\...

Homework Statement An open cylindrical tank of acid rests at the edge of a table 2.20\cdot 10^0\ m above the floor of the chemistry lab. If this tank springs a small hole in the side at its base, how far from the foot of the table will the acid hit the floor if the acid in the tank is...

Precisely.

Not true, endothermic reactions only remove heat from the system of the drink if the contents are evaporating. Since the higher energy molecules are literally flying out of the drink, the average energy of the drink is effectively lowered. Ice melting doesn't produce this effect because the...

Computing the derivative of an exponential function results in another exponential function, which doesn't really help when it comes to using L'Hopitals rule.

Homework Statement \lim_{n \to \infty}\frac{(-1)^{n+1} \cdot n^2}{n^2+1} Homework Equations \lim_{n \to \infty}a_n \neq 0 \rightarrow S \ is \ divergent The Attempt at a Solution I tried L'Hopital's rule, but I could not figure out how to find the limit of that pesky (-1)^{n+1}. Edit: This...

Thanks, I got the answer.

Homework Statement \frac{dy}{dx}=y^2-1 y(0)=3 Homework Equations \frac{dy}{dx}=f(y) \leftrightarrow \frac{dx}{dy}=\frac{1}{f(y)} The Attempt at a Solution \frac{dx}{dy}=\frac{1}{y^2-1} dx=\frac{dy}{y^2-1} \int dx=\int \frac{dy}{y^2-1}+C x=\int \frac{dy}{y^2-1}+C How do I integrate \int...

This.

So by Euler integration, do you mean using x=x_0+vdt rather than x=x_0+v{dt}+\frac{1}{2}a{dt}^2? Also, does the ball gain mechanical energy because the collision detection system flips both the ball's position with respect to the ground and the sign of the vertical component of the ball's...

In an excerpt from Ian Millington's Game Physics Engine Development, the author mentions a "damping" force: "In our physics engine we could simply assume that there are no forces at work and use [Newton's First Law] directly. To simulate drag we could add special drag forces. This is fine for...