# Search results

1. ### Rotational Dynamics

Homework Statement A wheel is spinning at n=1200rpm. The wheel starts to linearly decelerate, and after t=100s it stops. Determine the velocity, and acceleration of a point 10cm from the center of the mass, after 50 seconds of decelerating. The radius of the wheel is 30cm. Homework Equations...
2. ### Torque and vectors

Homework Statement So I was wondering how do we account for vectors that are at a certain angle. The problem that I'm having with the picture is: if I was calculating torque from point B, how would I account for the vector G. Homework Equations The Attempt at a Solution I've...
3. ### Conservation of energy - spring

Homework Statement Hello, I'm having a problem with this. So we drop the weight on this spring, and the question is: how much does the spring compress? The mass is 5kg, the height 0,4m, and the spring elasticity factor k=1700N/m. Homework Equations The Attempt at a Solution I've...
4. ### Multivariable domain

Homework Statement I'm having a problem with solving the domain of |x^2+y^2|<=|z^2|. Homework Equations The Attempt at a Solution From what I got this should be separated into two expressions: x^2+y^2<=z^2, and x^2+y^2>=-z^2. The later doesn't have a real solution because of the...
5. ### Series convergence problem

Homework Statement So I need to determine if the series \Sigmaln(1+e^{-n})/n converges. Homework Equations The Attempt at a Solution I know it does, but cannot prove it. Wolfram says that the ratio test indicates that the series converges, but when I try to solve the limit I get that it...
6. ### Falling functions

Homework Statement Hello, I was wondering if a falling function needs to fall on it's whole domain? I was solving a series with alternating sings. It says that if the series has alternating signs, that it converges if: 1) lim(n->0)an=0 2) an is a falling function I was solving this...
7. ### Integral solving problem

Homework Statement I've been trying to integrate the following: ∫\frac{cos^3(x)}{\sqrt{sin(x)}}dx Homework Equations The Attempt at a Solution First, I substituted sin(x) with t, and got dt=cos(x)dx => dx=\frac{dt}{cos(x)}. After that I got ∫\frac{cos^2(x)}{\sqrt{t}}dt Then i transformed...
8. ### Finite limit problem

Homework Statement I've read in my textbook, and confirmed via WolframAlpha that lim x->0 (cosx/x^0) =1 , and need an explanation for it. I thought it should be ∞ or something undefined, since 0^0 is undefined. Homework Equations The Attempt at a Solution I tried to use L'Hospitale on the...
9. ### Function domain help

Homework Statement Hello! Could someone explain some things presented in this example: http://i.imgur.com/wVOxf.png My friend, and I haven't been able to crack it. I get all the x-conditions right, but can't put the whole thing together into a domain. Here it's presented that xe[-2,3] due to...